Series route: This guide belongs to the complete PSLE Learner’s Guide volume directory. The original PSLE Learning Guide supplies the wider English, Mathematics and Science route, while PSLE Mathematics provide verified subject-specific continuation.
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This volume solves one precise learner problem: the learner guesses that ten factors means a tenth power or overlooks the mixed-prime form, instead of deriving every exponent pattern from the multiplicative partitions of ten. The goal is durable control, not a remembered slogan. A Primary 6 learner should be able to identify the trigger, explain the mechanism, perform the decision under time pressure and reject an attractive answer that exceeds the evidence.
- Start with the exact mistake and the evidence boundary.
- Build the mechanism before memorising a shortcut.
- Study worked contrasts and name why the near-miss fails.
- Repair misconceptions with one targeted check each.
- Attempt graded independent practice before reading the explanations.
- Return after a delay and prove that the method transfers.
- Use the parent and tutor notes after the learner has attempted the work.
The problem beneath the mistake
The number 512 has exactly ten positive factors because 512=2⁹. A divisor may use an exponent of 2 from 0 through 9, giving ten choices.
The number 48 also has ten factors because 48=2⁴×3. There are five choices for the exponent of 2 and two choices for the exponent of 3.
The divisor-count rule says that if n=pᵃqᵇ…, then the number of positive factors is (a+1)(b+1)… .
To classify exactly ten factors, factor ten as a product of integers at least two. The complete multiplicative partitions are 10 and 5×2.
Subtract one from each choice factor. Ten gives exponent 9; five by two gives exponents 4 and 1.
Therefore every qualifying number is p⁹ or p⁴q, where p and q are distinct primes in the mixed form.
The order of the named primes is flexible: either distinct prime may carry the fourth power. The exponent pattern, not the letter order, defines the structure.
Distinctness matters. If q=p, then p⁴q becomes p⁵, which has six factors rather than ten.
A prime tenth power has eleven factors, not ten, because the zero exponent is also a divisor choice.
Examples verify the forms, while the partitions of ten prove that no third structure exists.
Exactly excludes numbers with twelve, fifteen or any other count. Visual complexity is irrelevant unless the prime exponents produce the target choice product.
The reliable routine is prime-factorise, count choices, partition ten, subtract one, enforce distinctness and verify the converse.
Core decision: A positive whole number has exactly ten positive factors if and only if it is p⁹ or p⁴q, where p and q are distinct primes. The forms arise from the only multiplicative partitions 10 and 5×2.
Divisor counting is a problem of independent exponent choices. Factoring the desired count classifies every possible prime-exponent structure and replaces guessing with proof.
Mechanism: why the rule works
1. Factor completely
Write the number as distinct prime bases with combined exponents.
Composite or repeated bases can hide the true choice counts.
Diagnostic check. Are all bases prime and combined?
2. Count choices
An exponent a offers a+1 possibilities from zero through a.
Choices across distinct primes multiply.
Diagnostic check. What is the product of one-more-than-exponent terms?
3. Partition ten
List 10 and 5×2.
These are the only products of integers at least two equal to ten.
Diagnostic check. Has every multiplicative partition been used?
4. Translate ten
Choice factor 10 gives exponent 9.
This produces p⁹.
Diagnostic check. Did you subtract one?
5. Translate five by two
Choice factors 5 and 2 give exponents 4 and 1.
This produces p⁴q.
Diagnostic check. Are the two prime bases distinct?
6. Verify both forms
p⁹ gives 9+1=10; p⁴q gives (4+1)(1+1)=10.
The converse confirms sufficiency.
Diagnostic check. Does each candidate return exactly ten?
7. Prove completeness
Any additional prime base contributes another factor of at least two.
A third structure would require a missing partition of ten, which does not exist.
Diagnostic check. What count product would the claimed structure make?
Worked examples: make the decision visible
Pause before each answer. State the controlling evidence in one line, then complete the operation. The explanations deliberately contrast a valid route with a plausible but invalid one, because transfer grows when the learner can say why a tempting route does not apply.
Worked example 1: Forty-eight
Task. 48=2⁴×3.
Reasoning. The count is (4+1)(1+1)=10.
Answer. Forty-eight qualifies.
Independent check. It matches p⁴q.
Contrast-and-transfer pass. Keep the governing principle from “Forty-eight”, but change one surface detail in the task: 48=2⁴×3. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Forty-eight qualifies.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 2: Eighty
Task. 80=2⁴×5.
Reasoning. The count is 5×2=10.
Answer. Eighty qualifies.
Independent check. A different q preserves the pattern.
Contrast-and-transfer pass. Keep the governing principle from “Eighty”, but change one surface detail in the task: 80=2⁴×5. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Eighty qualifies.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 3: One hundred sixty-two
Task. 162=3⁴×2.
Reasoning. The count is 5×2=10.
Answer. One hundred sixty-two qualifies.
Independent check. The fourth-power prime need not be 2.
Contrast-and-transfer pass. Keep the governing principle from “One hundred sixty-two”, but change one surface detail in the task: 162=3⁴×2. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—One hundred sixty-two qualifies.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 4: Five hundred twelve
Task. 512=2⁹.
Reasoning. The exponent choices run from 0 to 9.
Answer. Five hundred twelve qualifies.
Independent check. It matches the single-prime form.
Contrast-and-transfer pass. Keep the governing principle from “Five hundred twelve”, but change one surface detail in the task: 512=2⁹. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Five hundred twelve qualifies.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 5: One thousand twenty-four
Task. 1024=2¹⁰.
Reasoning. The count is eleven.
Answer. It does not qualify.
Independent check. Exponent ten means eleven choices.
Contrast-and-transfer pass. Keep the governing principle from “One thousand twenty-four”, but change one surface detail in the task: 1024=2¹⁰. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It does not qualify.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 6: Thirty-two
Task. 32=2⁵.
Reasoning. The count is six.
Answer. It does not qualify.
Independent check. The exponent is too small for the single-prime form.
Contrast-and-transfer pass. Keep the governing principle from “Thirty-two”, but change one surface detail in the task: 32=2⁵. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It does not qualify.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 7: One hundred forty-four
Task. 144=2⁴×3².
Reasoning. The count is 5×3=15.
Answer. It does not qualify.
Independent check. The second exponent must be one.
Contrast-and-transfer pass. Keep the governing principle from “One hundred forty-four”, but change one surface detail in the task: 144=2⁴×3². Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It does not qualify.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 8: Repeated base
Task. p⁴×p=p⁵.
Reasoning. The count becomes six.
Answer. The mixed form requires q different from p.
Independent check. Combine repeated primes first.
Contrast-and-transfer pass. Keep the governing principle from “Repeated base”, but change one surface detail in the task: p⁴×p=p⁵. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The mixed form requires q different from p.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 9: Three distinct primes
Task. pqr has 2×2×2=8 factors.
Reasoning. It cannot produce ten.
Answer. Three first-power bases belong to a different classification.
Independent check. Use the choice product.
Contrast-and-transfer pass. Keep the governing principle from “Three distinct primes”, but change one surface detail in the task: pqr has 2×2×2=8 factors. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Three first-power bases belong to a different classification.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 10: Smallest
Task. Compare 2⁴×3=48 with 2⁹=512.
Reasoning. The mixed form gives the smaller candidate.
Answer. The smallest number with ten factors is 48.
Independent check. Both structures were considered.
Contrast-and-transfer pass. Keep the governing principle from “Smallest”, but change one surface detail in the task: Compare 2⁴×3=48 with 2⁹=512. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The smallest number with ten factors is 48.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 11: Unknown exponent
Task. If 3ᵃ has ten factors, solve a+1=10.
Reasoning. a=9.
Answer. The number is 3⁹.
Independent check. Substitution restores ten choices.
Contrast-and-transfer pass. Keep the governing principle from “Unknown exponent”, but change one surface detail in the task: If 3ᵃ has ten factors, solve a+1=10. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The number is 3⁹.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 12: Completeness
Task. Why not p²q?
Reasoning. Its factor count is 3×2=6.
Answer. It belongs to the six-factor structure.
Independent check. The count equation rejects it.
Contrast-and-transfer pass. Keep the governing principle from “Completeness”, but change one surface detail in the task: Why not p²q? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It belongs to the six-factor structure.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
The method lab: change one condition at a time
Build a controlled comparison around this problem: the learner guesses that ten factors means a tenth power or overlooks the mixed-prime form, instead of deriving every exponent pattern from the multiplicative partitions of ten. Write one clear case, one near-miss and one neighbouring case. Change only one decisive condition between adjacent examples. Predict first, then name the evidence that would reverse the decision. The boundary should become visible rather than remaining a memorised slogan.
Turn the central claim into a decision card: A positive whole number has exactly ten positive factors if and only if it is p⁹ or p⁴q, where p and q are distinct primes. The forms arise from the only multiplicative partitions 10 and 5×2. Put the trigger question on the front. On the back, write the mechanism, one worked example, one near-miss and the limit. Test both directions: rule to example and example to rule.
Make an evidence ladder with four rungs: observation or given information, interpreted relationship, conclusion and independent check. If two rungs repeat the same idea, rewrite one so it performs a distinct job. Strong reasoning moves forward rather than echoing the question.
Construct two tempting wrong answers. Identify the exact decision where each fails, explain why it looks plausible and write the smallest repair. Change the surface details and repeat so the correction transfers beyond one familiar item.
Teach the idea aloud in ninety seconds without notes. Include the controlling condition, mechanism, example, near-miss and one sentence beginning “This does not mean…”. Repair only the missing link, then teach the complete chain again more concisely.
After two days, attempt one direct item, one disguised item and one item where the rule should not be used. Write the method choice before solving. After one week, rebuild the rule on a blank page and verify it by a different route.
Common misconceptions and targeted repairs
Misconception 1: Tenth power
What the learner may think. Ten factors means p¹⁰.
Why it fails. p¹⁰ has eleven factors.
Targeted repair. Include exponent zero and subtract one.
Misconception 2: Only p⁹
What the learner may think. The mixed form is missed.
Why it fails. Ten also factors as 5×2.
Targeted repair. List all partitions.
Misconception 3: p⁴q with equal bases
What the learner may think. q may equal p.
Why it fails. The bases combine to p⁵.
Targeted repair. Require distinct primes.
Misconception 4: Any product with power four
What the learner may think. p⁴ times a composite is accepted.
Why it fails. The second factor must be a distinct prime in complete factorisation.
Targeted repair. Factor q if necessary.
Misconception 5: Add choices
What the learner may think. Five and two are added to get seven.
Why it fails. Independent choices multiply to ten.
Targeted repair. Use a grid or product rule.
Misconception 6: Examples prove all
What the learner may think. Several qualifying values establish completeness.
Why it fails. Only the partitions of ten exclude other forms.
Targeted repair. Write the count equation.
Misconception 7: At least ten
What the learner may think. A number with fifteen factors is accepted.
Why it fails. Exactly ten excludes it.
Targeted repair. Underline the quantifier.
Misconception 8: Letter order creates new form
What the learner may think. p⁴q and pq⁴ are treated as different structures.
Why it fails. They share exponent pattern 4,1.
Targeted repair. Name which prime carries the fourth power without inventing a new case.
Graded independent practice with explained answers
Attempt each item without looking ahead. Write the evidence or relationship before the final response. Early items check recognition; middle items require explanation; later items change the surface form so that copying a worked example is insufficient.
Practice 1: Rule
Question. State both forms.
Explained answer. p⁹ or p⁴q with distinct primes.
Why this earns trust. The classification is complete.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “p⁹ or p⁴q with distinct primes.” from memory, but to recreate a justified answer from the new evidence.
Practice 2: Forty-eight
Question. Does 48 qualify?
Explained answer. Yes.
Why this earns trust. 2⁴×3 gives ten choices.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Yes.” from memory, but to recreate a justified answer from the new evidence.
Practice 3: Eighty
Question. Does 80 qualify?
Explained answer. Yes.
Why this earns trust. 2⁴×5 gives ten factors.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Yes.” from memory, but to recreate a justified answer from the new evidence.
Practice 4: Five hundred twelve
Question. Does 512 qualify?
Explained answer. Yes.
Why this earns trust. 2⁹ has ten factors.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Yes.” from memory, but to recreate a justified answer from the new evidence.
Practice 5: One thousand twenty-four
Question. How many factors?
Explained answer. Eleven.
Why this earns trust. It is 2¹⁰.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Eleven.” from memory, but to recreate a justified answer from the new evidence.
Practice 6: Thirty-two
Question. How many factors?
Explained answer. Six.
Why this earns trust. It is 2⁵.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Six.” from memory, but to recreate a justified answer from the new evidence.
Practice 7: Distinctness
Question. Why must p and q differ?
Explained answer. Otherwise p⁴q becomes p⁵ and has six factors.
Why this earns trust. Repeated bases combine.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Otherwise p⁴q becomes p⁵ and has six factors.” from memory, but to recreate a justified answer from the new evidence.
Practice 8: Partitions
Question. List the count partitions.
Explained answer. 10 and 5×2.
Why this earns trust. No structure is omitted.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “10 and 5×2.” from memory, but to recreate a justified answer from the new evidence.
Practice 9: Translate
Question. What exponents follow from 5×2?
Explained answer. 4 and 1.
Why this earns trust. Subtract one from each factor.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “4 and 1.” from memory, but to recreate a justified answer from the new evidence.
Practice 10: Three primes
Question. Does 30 have ten factors?
Explained answer. No, it has eight.
Why this earns trust. 2×3×5 gives 2³ choices.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “No, it has eight.” from memory, but to recreate a justified answer from the new evidence.
Practice 11: Smallest
Question. What is the smallest qualifying number?
Explained answer. 48.
Why this earns trust. Compare the least candidates from both forms.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “48.” from memory, but to recreate a justified answer from the new evidence.
Practice 12: Unknown
Question. Find a if pᵃ has ten factors.
Explained answer. a=9.
Why this earns trust. a+1=10.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “a=9.” from memory, but to recreate a justified answer from the new evidence.
Practice 13: Converse
Question. Why does p⁴q work?
Explained answer. Five choices for p and two for q multiply to ten.
Why this earns trust. Sufficiency is checked.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Five choices for p and two for q multiply to ten.” from memory, but to recreate a justified answer from the new evidence.
Practice 14: Routine
Question. State the method.
Explained answer. Factor, count, partition, translate, distinguish primes and verify.
Why this earns trust. Every step blocks a common error.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Factor, count, partition, translate, distinguish primes and verify.” from memory, but to recreate a justified answer from the new evidence.
A four-session mastery cycle
Session 1: construct. Read the mechanism once, cover it and write a three-line model containing the trigger, the operation and the check. Add one example and one near-miss. Compare only after the model is complete. If the operation is right but the trigger is missing, the knowledge is unsafe because it may be applied in the wrong place.
Session 2: discriminate. Mix six items: two that clearly require this method, two that tempt the method but violate a condition, and two that require another skill. For every item, write “use” or “do not use” before answering. Accuracy in method selection matters more than speed at this stage.
Session 3: explain. Give a complete answer to an imagined classmate. Include the smallest sufficient evidence, the mechanism and the independent check. Remove any sentence that merely repeats the question or adds an unsupported claim. A concise causal explanation is stronger than a longer collection of familiar words.
Session 4: perform. Attempt a timed mixed set without notes. Mark uncertain decisions, but continue. During review, classify each error as trigger, evidence, operation, scope, unit or check. Reattempt one changed version after a delay. Mastery is shown when the learner chooses and adapts the method without needing the original example beside it.
Delayed transfer: prove that the learning lasts
Transfer test 1: Changed context
Apply the idea in a fresh context after two days.
Success criterion. Trigger, mechanism and limit are stated.
Transfer test 2: Near-miss audit
Explain why a tempting example fails.
Success criterion. The exact failed condition is named.
Transfer test 3: Independent check
Verify by a second route.
Success criterion. The check does not repeat the same mistake.
Transfer test 4: Blank recall
Rebuild the idea after one week.
Success criterion. Definition, example, near-miss and boundary appear.
Examination control
1. Prime-factorise completely. Combine repeated bases before counting.
2. Form the choice product. Use one more than each exponent.
3. Partition ten. Use both 10 and 5×2.
4. State distinctness. The mixed form needs different prime bases.
5. Verify exactly. Return to the count formula.
Under time pressure, compress the method to undefined. The compressed routine is useful only after the full reasoning is understood. If it produces uncertainty, expand the step instead of guessing.
A compact error log
Label the failed decision rather than writing “careless”. A precise error label makes the next practice item useful.
Reattempt one changed version after a delay. Mastery requires method selection, not recognition of the original wording.
Notes for parents and tutors
Ask for controlling evidence before accepting the answer.
Let the learner attempt a near-miss before explaining again.
Praise precise limits and checks, not speed alone.
Use fresh contexts so the decision transfers.
Frequently asked questions
What are the two forms?
p⁹ and p⁴q.
Why only two?
Ten has only the multiplicative partitions 10 and 5×2 using parts at least two.
Must the primes differ?
Yes.
What is the smallest example?
48.
Does 80 qualify?
Yes.
Does 512 qualify?
Yes.
Why not p¹⁰?
It has eleven factors.
What is the general rule?
Multiply one more than every prime exponent.
Next routes
Return to the complete volume directory to locate the series, use the original PSLE Learning Guide for the foundation route, and continue through PSLE Mathematics for verified subject guidance. The next useful task is a mixed set in which this idea is sometimes relevant and sometimes irrelevant; that is where the learner must choose a method rather than imitate one.