PSLE Learner’s Guide · Vol 0362 · Factors, multiples, divisibility and constrained search
Find the exact decision this guide helps you make
This guide helps a Primary 6 learner find a missing digit efficiently by translating each divisibility statement into a constraint, intersecting the possible digits and verifying the completed number. The short rule is convert every divisibility condition into allowed digits, intersect the sets, then test the complete number. You will learn the mechanism, see worked examples, repair common misconceptions, practise in stages and use a compact examination routine.
Choose a reading route
- Understand why the error happens
- Use the step-by-step method
- Study eight worked cases
- Build practice and delayed transfer
- Use the examination-control routine
- Guidance for parents and tutors
- Read the FAQs and choose the next route
This is an examination-performance guide, not a replacement for full topic teaching. Use the complete PSLE Learner’s Guide volume directory to move across this series, the PSLE Learning Guide for the wider sequence and the Mathematics Learning Hub for deeper subject instruction.
For complete teaching, worked practice and topic progression beyond this performance decision, continue through the Mathematics Learning Hub. The PSLE factors-and-multiples learning guide gives a focused canonical explanation of the underlying topic. This volume keeps a narrower job: it helps the learner recognise, execute and check one examination decision without competing with the wider topic owner. For a nearby performance routine that is already published, continue to Vol 0350 on finding one ratio unit from a total.
A careful note about the current examination year
This article is written for the 2026 PSLE preparation context. SEAB’s official 2026 formats page lists English Language as subject 0001, revised Mathematics as 0008 and revised Science as 0009. Format details can change, so confirm any paper-specific timing, component or administrative instruction with the current official SEAB 2026 source and your school. The reasoning routine taught here is deliberately broader: it strengthens how you read evidence, make a decision and check an answer.
Why this mistake happens
A box inside a number invites random trial, but a missing digit is rarely an invitation to guess ten times. Divisibility conditions describe what the ones digit, last two digits or digit sum must do. Each condition removes impossible digits. When two conditions apply, their allowed sets must intersect. The strongest method therefore starts with the cheapest restriction, records all surviving digits, applies the next condition and checks the complete number. This avoids both wasteful enumeration and the common mistake of stopping at the first value that works.
The mind likes a fast label. A familiar word, operation, result or rule triggers an answer before the conditions have been checked. That shortcut sometimes works in easy practice, so it becomes a habit. In a demanding question, however, a nearby distractor preserves the surface pattern while changing one important condition. The learner then performs a correct-looking move on the wrong object. The repair is to slow only the decision point: identify what is being linked or measured, preserve its labels, test the conditions, and then continue at normal speed.
Think of the method as a chain with four locks. Object: what exact idea or quantity is under discussion? Relationship: how are the relevant parts connected? Condition: what must be true for the move to be valid? Claim: what is the strongest conclusion the evidence actually supports? A weak answer often skips from object to claim. A strong answer makes the two middle locks visible.
The one-line operating rule
Convert every divisibility condition into allowed digits, intersect the sets, then test the complete number. Say it before the first practice set. During timed work, shorten it to four cue words you can recall without stopping.
The step-by-step method
Step 1: Copy the number with the missing place clearly labelled and list the possible digits from zero to nine
Copy the number with the missing place clearly labelled and list the possible digits from zero to nine. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 2: Translate each stated divisor into its usable test, such as an even last digit or a digit sum divisible by three or nine
Translate each stated divisor into its usable test, such as an even last digit or a digit sum divisible by three or nine. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 3: Apply the condition that removes the most possibilities with the least calculation
Apply the condition that removes the most possibilities with the least calculation. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 4: Intersect the surviving sets when more than one divisibility condition is given
Intersect the surviving sets when more than one divisibility condition is given. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 5: Respect place-value limits, including that a leading digit of a stated multi-digit number cannot be zero
Respect place-value limits, including that a leading digit of a stated multi-digit number cannot be zero. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 6: Substitute every survivor into the complete number and divide or use a second check before claiming uniqueness
Substitute every survivor into the complete number and divide or use a second check before claiming uniqueness. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Misconceptions to diagnose and repair
Misconception 1
Tempting move: Trying digits in order and stopping at the first success. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 2
Tempting move: Using the digit-sum test for a divisor to which it does not apply. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 3
Tempting move: Forgetting that zero can fill an internal digit but not a leading place in a stated multi-digit number. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 4
Tempting move: Checking divisibility by two and three separately but forgetting that both are needed for divisibility by six. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 5
Tempting move: Claiming one answer when the information permits several digits. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Eight worked cases
Worked case 1: Divisible by three
Scenario. Find all digits in 4□2 that make the number divisible by 3.
The tempting error. Trying one digit and reporting it as unique. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The known digit sum is 6, so the missing digit must make 6+□ a multiple of 3. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The digits are 0, 3, 6 and 9. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Verify 402, 432, 462 and 492. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 2: Divisible by nine
Scenario. Find the digit in 57□ if the number is divisible by 9.
The tempting error. Looking only at the ones digit. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The digit sum is 12+□. The only digit making a nearby multiple of 9 is 6, giving 18. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The missing digit is 6. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Check 576÷9=64. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 3: Divisible by five
Scenario. Find possible digits in 8□5 if the number is divisible by 5.
The tempting error. Assuming the middle digit is five. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. Divisibility by 5 depends only on a last digit of 0 or 5. The last digit is already 5. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Every digit 0 to 9 is possible in the tens place. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Explain why the condition does not create a unique answer. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 4: Divisible by ten and three
Scenario. Find digits in 6□0 that make the number divisible by 10 and 3.
The tempting error. Using the zero only to conclude the job is complete. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The final zero satisfies divisibility by 10. For divisibility by 3, 6+□ must be a multiple of 3. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The digits are 0, 3, 6 and 9. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Check both conditions for each completed number. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 5: Leading digit
Scenario. Find possible □ in □24 if the three-digit number is divisible by 4.
The tempting error. Including zero because 24 is divisible by 4. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The last two digits 24 make every choice divisible by 4, but a three-digit number needs a non-zero hundreds digit. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The digits are 1 through 9. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. State why zero changes the number of digits. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 6: Divisible by six
Scenario. Find digits in 3□6 that make the number divisible by 6.
The tempting error. Checking only that the final digit is even. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. A number divisible by 6 must be divisible by 2 and 3. The final 6 handles 2; 9+□ must be divisible by 3. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The digits are 0, 3, 6 and 9. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Divide one completed number by 6. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 7: Two different tests
Scenario. Find □ in 2□4 if the number is divisible by both 3 and 4.
The tempting error. Adding the digits for both tests. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The last two digits □4 must be divisible by 4, while 6+□ must be divisible by 3. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. The shared possibilities are 2 and 8, giving 224 and 284. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Check both completed numbers by division. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 8: Rejecting false uniqueness
Scenario. A learner says 1□8 divisible by 3 must be 138.
The tempting error. Accepting the first working completion. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The digit sum 9+□ must be divisible by 3, so □ can be 0, 3, 6 or 9. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. 108, 138, 168 and 198 all work. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Write the full solution set before deciding whether the answer is unique. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Practice progression: from recognition to transfer
Round 1: mark only
Use six short items. Do not answer them. Mark the object, reference, unit, interval, condition or rule that controls the decision. The goal is accurate noticing without the burden of full writing.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 2: explain the choice
Solve four items and add one sentence beginning “This is valid because…”. If the sentence merely repeats the answer, the condition is still hidden.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 3: repair a wrong answer
Take four plausible wrong answers. Identify the earliest faulty link, preserve the correct work and rewrite only what must change. This develops error diagnosis rather than answer copying.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 4: mixed questions
Mix this job with two older skills. Remove headings that reveal the topic. Decide which routine applies before solving. Selection is part of performance.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 5: timed set
Use a small timed set with a fixed check budget. Mark a cue at the decision point, finish the answer, then perform one positive check and one rejection check.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 6: delayed transfer
Return after two or three days with different surface details. Before seeing notes, write the one-line rule from memory and solve. Compare the new error pattern with the earlier one.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Graded independent practice with explained answers
Practice 1: Foundation
Try it. Find all digits in 2□1 that make the number divisible by 3.
Open the answer and explanation after attempting the question
Answer. 0, 3, 6 and 9.
Why. The known sum is 3, so the missing digit must be a multiple of 3.
Check or transfer. Check all four completions.
Practice 2: Divisible by nine
Try it. Find □ in 63□ if the number is divisible by 9.
Open the answer and explanation after attempting the question
Answer. 0 or 9.
Why. The known sum is 9, so totals 9 and 18 both work.
Check or transfer. Do not assume uniqueness.
Practice 3: Last two digits
Try it. Find all □ in 5□2 if the number is divisible by 4.
Open the answer and explanation after attempting the question
Answer. 1, 3, 5, 7 and 9.
Why. The last two digits can be 12, 32, 52, 72 or 92.
Check or transfer. Divide each two-digit ending by 4.
Practice 4: Combined test
Try it. Find □ in 4□8 if the number is divisible by 6.
Open the answer and explanation after attempting the question
Answer. 0, 3, 6 or 9.
Why. The number is already even; 12+□ must be divisible by 3.
Check or transfer. Verify one by long division.
Practice 5: Two constraints
Try it. Find □ in 7□2 if the number is divisible by both 3 and 4.
Open the answer and explanation after attempting the question
Answer. 3 or 9.
Why. For 4, □2 permits odd tens digits; for 3, 9+□ must be divisible by 3. The intersection is 3 and 9.
Check or transfer. Check 732 and 792.
Practice 6: Delayed transfer
Try it. After two days, decide whether “one digit only” is guaranteed for □45 divisible by 5.
Open the answer and explanation after attempting the question
Answer. No; any non-zero leading digit 1 to 9 works.
Why. The final digit 5 already satisfies the only stated test, and the leading-place rule merely removes zero.
Check or transfer. Explain why more information is needed for uniqueness.
A compact practice log
- Question source and date
- Decision cue you marked
- Your first answer in one line
- Earliest wrong link, if any
- Corrected rule in twelve words or fewer
- Date for delayed transfer
- Whether the new item was solved without notes
A useful log is small enough to maintain. It should help you predict the next mistake, not become a scrapbook of completed pages.
Checking that tests meaning, not neatness
A check should have a target. First run a positive test: identify the evidence, calculation or condition that supports your answer. Then run a rejection test: name the closest tempting alternative and the exact reason it fails. This pair is more powerful than rereading the same line while hoping to feel certain.
Use a reverse check where possible. Reconstruct the original amount, replace a connector with its expanded meaning, map a conclusion back to the data, or apply the repaired rule to the apparent exception. Reverse checking exposes lost labels and unsupported leaps because the answer has to return to its source.
Stop when the check has answered a real question. Repeatedly changing a sound answer because it feels unfamiliar is not checking. If the object, relationship, condition and claim all remain consistent, keep the answer and move on.
Examination control
When time is tight, use the cue ORCC: Object, Relationship, Condition, Claim. Write only the smallest useful mark—an arrow, a unit, a time interval, a boundary or a qualifying word. The mark should prevent the known error without slowing the rest of the paper.
- Read the command word and identify the decision.
- Mark the object or quantity that must keep its identity.
- State the relationship or operation in plain language.
- Check the condition that makes it valid.
- Give the claim at the strength supported by evidence.
- Use one positive and one rejection check, then stop.
If you become stuck, do not produce a longer answer immediately. Shorten the task: write what is known, what must be decided and what condition separates the two best options. A precise partial structure often unlocks the next step and also makes any partial credit more defensible.
A seven-day delayed-transfer plan
- Day 1: learn the one-line rule and complete two worked cases with notes.
- Day 2: solve four short items without notes; classify errors by N, M, I or C.
- Day 3: mix two new items with two older PSLE skills and hide the topic labels.
- Day 4: explain one case aloud to a parent, tutor or imaginary learner in under two minutes.
- Day 5: complete a timed mini-set and use the ORCC marks only at decision points.
- Day 6: rest this skill or practise a different subject so memory has to consolidate.
- Day 7: attempt one unfamiliar transfer item, then write the smallest rule revision needed.
Success on Day 7 matters more than fluency immediately after reading. Delayed transfer shows whether you can retrieve the method, recognise its job under new surface details and control it without a model beside you.
Guidance for parents and tutors
Ask for the decision, not a performance speech. Useful prompts are: “What exactly are you deciding?”, “Which word, unit or condition controls it?”, “What is the closest wrong option?” and “How can you check without starting again?” These questions keep ownership with the learner while making thinking visible.
When an error occurs, locate its earliest point. Praise accurate diagnosis even before the final answer is corrected. If the learner repeatedly loses the same label, introduce one stable notation: arrows for reference, units beside remainders, interval brackets for rates, or boxes around claim conditions. Avoid adding several new routines at once.
Build variation gradually. Begin with clean examples, then add one plausible distractor, then mix the skill with older content, and finally delay the next attempt. A learner who succeeds only when the worksheet title names the method has learned recognition, not transfer.
Keep emotional temperature low. A surprising exception or remainder is information, not proof that the learner is “bad at” a subject. The practical question is which link changed. Once that link is named, practise a small set that isolates it and then return to mixed questions.
The independent-reader test
Before you call the skill secure, explain one solution to a reader who cannot see your thoughts. Name the starting information, the decision, the condition that controls it and the reason the rejected alternative fails. If the explanation depends on “you know what I mean”, a label is still missing. Add that label to the answer, then remove any sentence that does not help the reader follow the chain.
Next, cover the worked example and rebuild the method from a fresh prompt. Do not copy the surface details. Recover the sequence of decisions. This separates genuine control from familiarity with one page. A learner who can transfer the decision routine to new names, numbers or apparatus has a more dependable examination skill than a learner who can reproduce only the model answer.
Finally, compress the method without losing its safety condition. Write one sentence of no more than fifteen words, then test that sentence against an awkward case. If the short rule gives the wrong result, restore the missing condition. Good compression keeps the mechanism available under time pressure while the awkward case prevents the cue from becoming a careless shortcut.
A timed diagnosis drill
Set aside twelve minutes and choose three unfamiliar questions that could trigger this error. Spend the first minute identifying the decision in each question without solving it. Mark the object, relationship, condition and permitted claim. This preview is not wasted time: it prevents you from entering a long method before you know what the method must preserve.
Solve the three questions in the next eight minutes. After each answer, write one tiny prediction about what a correct answer should preserve: a reference word, a whole-number boundary, a pathway, a unit, a direction or an observable result. Then compare the finished answer with that prediction. If they disagree, repair the earliest link and keep the later work only when its meaning remains valid.
Use the final three minutes to classify the errors. A noticing error means the controlling detail was never marked. A method error means the right information was present but the wrong operation or reasoning chain was used. An interpretation error means the result was calculated or observed correctly but described at the wrong level. A checking error means the answer contained a detectable contradiction that the final audit missed.
Repeat the drill a week later with different surface details and without looking at the old corrections. Improvement is not merely a higher score. Look for a shorter pause at the decision point, fewer unnecessary restarts, more stable labels and a clearer reason for rejecting the nearest wrong answer. Those are signs that the performance routine is becoming portable.
Frequently asked questions
Why not try all ten digits immediately?
Divisibility tests remove impossible values quickly and make the reasoning visible.
Can zero be a missing digit?
Yes in an internal or final place unless another condition excludes it; not as the leading digit of a stated multi-digit number.
What is the divisibility test for 3?
The sum of the digits must be divisible by 3.
What is the test for 4?
The number formed by the last two digits must be divisible by 4.
What is the test for 6?
The number must be divisible by both 2 and 3.
How do I know an answer is unique?
Only one digit remains after every condition and place-value restriction is applied.
Should I still verify?
Yes. Substitute the digit and check the complete number.
What should I study next?
Use the Mathematics Learning Hub and factors-and-multiples guide for broader divisibility and factor work.
Your next route
Use this guide until you can state the rule, solve an unfamiliar case and explain why the closest alternative fails. Then return to the complete PSLE Learner’s Guide volume directory or move to a deeper subject route: the English Learning Hub, Mathematics Learning Hub, Science Learning Hub, or the full learning-hubs directory. Return to the PSLE Learning Guide when you want to place this skill inside a broader revision sequence.
Mathematics turns the batch’s meaning test into a constrained search: every statement has a precise consequence, and only digits satisfying all consequences survive.