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 searches by listing factors and misses the proof that exactly seven positive factors forces one prime exponent of six, because seven is itself prime. 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 64 has the seven positive factors 1, 2, 4, 8, 16, 32 and 64. Its prime form is 2⁶.
For a number n=pᵃqᵇ…, every positive divisor is formed by choosing an exponent for each prime. The number of choices is (a+1)(b+1)… .
To obtain exactly seven factors, this product must equal 7. Because 7 is prime, it cannot be written as a product of two integers greater than 1.
Therefore there can be only one prime base in the factorisation, with a+1=7 and hence a=6.
Every valid number has the form p⁶, where p is prime. Conversely, p⁶ has the seven divisors p⁰ through p⁶.
This is an if-and-only-if classification: the form is necessary and sufficient. Examples alone would not prove that no other structure works.
The smallest example is 2⁶=64. The next is 3⁶=729, which is much larger because powers grow quickly.
A composite base must be prime-factorised first. For example, 4⁶ is not one prime to the sixth power; it equals 2¹² and has thirteen factors.
The wording exactly matters. A number with eight factors does not qualify even though it has at least seven.
Do not confuse the exponent with the factor count. p⁷ has eight positive factors, while p⁶ has seven.
A complete solution states the prime form, solves the exponent-choice equation and checks the converse.
The reliable routine is prime-factorise, multiply exponent choices, set the product to seven, use the primality of seven and verify.
Core decision: A positive whole number has exactly seven positive factors if and only if it is p⁶ for a prime p. The divisor-count product equals the prime number seven, so only one exponent-choice factor is possible.
Divisor counting is a choice problem. Factoring the desired divisor count classifies every possible prime-exponent structure and replaces incomplete trial listing with proof.
Mechanism: why the rule works
1. Prime-factorise fully
Write the number with prime bases and combined exponents.
Composite bases can hide the true exponent pattern.
Diagnostic check. Are all bases prime and distinct?
2. Count choices
For each exponent a, a divisor may use 0 through a.
That gives a+1 independent choices.
Diagnostic check. What is the product of choices?
3. Set the target
Require (a+1)(b+1)…=7.
The word exactly turns the problem into an equality.
Diagnostic check. Is the target seven, not at least seven?
4. Use primality
Seven has no product decomposition into integers greater than one.
Only one prime base can appear.
Diagnostic check. Why are two bases impossible?
5. Recover the exponent
Solve a+1=7.
The exponent is six.
Diagnostic check. Did you subtract one?
6. Check the converse
List exponents 0 through 6 for p⁶.
They produce exactly seven divisors.
Diagnostic check. Has sufficiency been shown?
7. Audit the base
Require p to be prime.
A composite base splits into more prime structure.
Diagnostic check. Was a composite base disguised?
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: Sixty-four
Task. 64=2⁶.
Reasoning. Count=6+1=7.
Answer. It qualifies.
Independent check. Its factor list confirms the formula.
Contrast-and-transfer pass. Keep the governing principle from “Sixty-four”, but change one surface detail in the task: 64=2⁶. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It 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: Seven hundred twenty-nine
Task. 729=3⁶.
Reasoning. Count=7.
Answer. It qualifies.
Independent check. The second example is already much larger.
Contrast-and-transfer pass. Keep the governing principle from “Seven hundred twenty-nine”, but change one surface detail in the task: 729=3⁶. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It 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 twenty-eight
Task. 128=2⁷.
Reasoning. Count=8.
Answer. It does not qualify.
Independent check. Exponent seven means eight choices.
Contrast-and-transfer pass. Keep the governing principle from “One hundred twenty-eight”, but change one surface detail in the task: 128=2⁷. 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 4: Thirty-two
Task. 32=2⁵.
Reasoning. Count=6.
Answer. It does not qualify.
Independent check. The exponent is one too small.
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 5: Four to the sixth
Task. 4⁶=(2²)⁶=2¹².
Reasoning. Count=13.
Answer. It does not qualify.
Independent check. The base was not prime.
Contrast-and-transfer pass. Keep the governing principle from “Four to the sixth”, but change one surface detail in the task: 4⁶=(2²)⁶=2¹². 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: Two prime bases
Task. n=pᵃqᵇ with positive exponents.
Reasoning. Each choice factor is at least 2, so their product is composite and at least 4.
Answer. It cannot equal prime 7.
Independent check. This excludes every two-base form.
Contrast-and-transfer pass. Keep the governing principle from “Two prime bases”, but change one surface detail in the task: n=pᵃqᵇ with positive exponents. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It cannot equal prime 7.—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: Three prime bases
Task. The minimum count is 2×2×2=8.
Reasoning. Seven is impossible.
Answer. No three-base form works.
Independent check. The lower bound is enough.
Contrast-and-transfer pass. Keep the governing principle from “Three prime bases”, but change one surface detail in the task: The minimum count is 2×2×2=8. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—No three-base form works.—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: Smallest value
Task. Choose the smallest prime in p⁶.
Reasoning. 2⁶=64.
Answer. Sixty-four is the smallest.
Independent check. The structure makes the search finite.
Contrast-and-transfer pass. Keep the governing principle from “Smallest value”, but change one surface detail in the task: Choose the smallest prime in p⁶. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Sixty-four is the smallest.—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: Reverse construction
Task. Build a seven-factor number divisible by 5.
Reasoning. Use 5⁶=15625.
Answer. It has seven factors.
Independent check. No second prime may be introduced.
Contrast-and-transfer pass. Keep the governing principle from “Reverse construction”, but change one surface detail in the task: Build a seven-factor number divisible by 5. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It has seven factors.—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: Factor-pair check
Task. 64 is a square.
Reasoning. Its factors pair around 8, with 8 paired with itself.
Answer. An odd factor count is consistent with a perfect square.
Independent check. Pairing checks but does not classify alone.
Contrast-and-transfer pass. Keep the governing principle from “Factor-pair check”, but change one surface detail in the task: 64 is a square. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—An odd factor count is consistent with a perfect square.—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: Exact versus at least
Task. 128 has eight factors.
Reasoning. It satisfies at least seven but not exactly seven.
Answer. Read the demand before solving.
Independent check. Inequality and equality differ.
Contrast-and-transfer pass. Keep the governing principle from “Exact versus at least”, but change one surface detail in the task: 128 has eight factors. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Read the demand before solving.—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: Proof completion
Task. Why are examples insufficient?
Reasoning. They show possible cases but cannot exclude another structure.
Answer. The equation and primality exclude all alternatives.
Independent check. Necessity and sufficiency are both present.
Contrast-and-transfer pass. Keep the governing principle from “Proof completion”, but change one surface detail in the task: Why are examples insufficient? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The equation and primality exclude all alternatives.—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 precise problem: the learner searches by listing factors and misses the proof that exactly seven positive factors forces one prime exponent of six, because seven is itself prime. Write one case that clearly satisfies the rule, one near-miss and one neighbouring case. Change only one important condition between adjacent cases. Predict first, then name the evidence that would reverse the decision. This makes the boundary usable instead of leaving it as a slogan.
Turn the central claim into a decision card: A positive whole number has exactly seven positive factors if and only if it is p⁶ for a prime p. The divisor-count product equals the prime number seven, so only one exponent-choice factor is possible. On the front, write only the trigger question. On the back, write the mechanism, a worked example, a near-miss and the limit of the claim. Test the card in both directions so an example can trigger the rule and the rule can generate a fresh example.
Make an evidence ladder with four rungs: observation or given information, interpreted relationship, conclusion and independent check. Complete every rung for a fresh item. If two rungs merely repeat the same words, rewrite one so it performs a different job. A strong explanation moves from what is known to why it matters and then checks the result independently.
Construct two tempting wrong answers deliberately. Identify the exact decision at which each answer fails, explain why it can look reasonable, and write the smallest repair that restores valid reasoning. Change the surface details and repeat. This develops error recognition without making the learner depend on the wording of one familiar question.
Teach the idea aloud in ninety seconds without notes. Include the controlling condition, the mechanism, one precise example, one near-miss and one sentence beginning with “This does not mean…”. Record the missing link, study only that link, then teach the complete chain again in fewer and clearer words.
After two days, attempt a mixed set containing one direct item, one disguised item and one item for which the rule should not be used. Write a one-line method choice before solving. After one week, rebuild the rule from a blank page and use a different check. Delayed transfer matters because immediate recognition can hide weak independent retrieval.
Common misconceptions and targeted repairs
Misconception 1: Exponent seven
What the learner may think. Seven factors means p⁷.
Why it fails. p⁷ has eight exponent choices.
Targeted repair. Subtract one from the target.
Misconception 2: Any sixth power
What the learner may think. The base may be composite.
Why it fails. The base must be prime after full factorisation.
Targeted repair. Prime-factorise the base.
Misconception 3: Two primes possible
What the learner may think. A mixed product might still give seven.
Why it fails. Seven is prime, so it has no 2×integer decomposition.
Targeted repair. Use the count product.
Misconception 4: Add choices
What the learner may think. Exponent-choice counts are added.
Why it fails. Independent prime choices multiply.
Targeted repair. Build a choice grid.
Misconception 5: List proves all
What the learner may think. One complete factor list is treated as classification.
Why it fails. It proves one example only.
Targeted repair. Solve the general equation.
Misconception 6: At least accepted
What the learner may think. Eight factors is accepted.
Why it fails. Exactly seven excludes eight.
Targeted repair. Underline the quantifier.
Misconception 7: Prime value seven
What the learner may think. The number itself must be 7.
Why it fails. A prime has only two factors.
Targeted repair. Distinguish target count from value.
Misconception 8: Odd count unexplained
What the learner may think. Odd factor count seems impossible because factors pair.
Why it fails. A square has one central self-paired factor.
Targeted repair. Identify p³ as the square root of p⁶.
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 the complete form.
Explained answer. p⁶ for prime p.
Why this earns trust. Both exponent and base condition appear.
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 “p⁶ for prime p.” from memory, but to recreate a justified answer from the new evidence.
Practice 2: 64
Question. How many factors?
Explained answer. Seven.
Why this earns trust. 64=2⁶.
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 “Seven.” from memory, but to recreate a justified answer from the new evidence.
Practice 3: 729
Question. Does it qualify?
Explained answer. Yes.
Why this earns trust. 729=3⁶.
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: 128
Question. How many factors?
Explained answer. Eight.
Why this earns trust. 128=2⁷.
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 “Eight.” from memory, but to recreate a justified answer from the new evidence.
Practice 5: 32
Question. How many factors?
Explained answer. Six.
Why this earns trust. 32=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 6: Composite base
Question. Does 4⁶ qualify?
Explained answer. No.
Why this earns trust. It equals 2¹² and has thirteen 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 “No.” from memory, but to recreate a justified answer from the new evidence.
Practice 7: Two bases
Question. Why impossible?
Explained answer. Their choice product would factor into at least two integers above one.
Why this earns trust. It cannot equal prime 7.
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 “Their choice product would factor into at least two integers above one.” from memory, but to recreate a justified answer from the new evidence.
Practice 8: Smallest
Question. What is the smallest qualifying number?
Explained answer. 64.
Why this earns trust. Use the smallest prime base.
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 “64.” from memory, but to recreate a justified answer from the new evidence.
Practice 9: Divisible by 3
Question. Give one example.
Explained answer. 3⁶=729.
Why this earns trust. The form is applied.
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 “3⁶=729.” from memory, but to recreate a justified answer from the new evidence.
Practice 10: Exact
Question. Does a number with eight factors qualify?
Explained answer. No.
Why this earns trust. Exactly is preserved.
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.” from memory, but to recreate a justified answer from the new evidence.
Practice 11: Converse
Question. Why does p⁶ work?
Explained answer. Allowed exponents are 0,1,2,3,4,5,6.
Why this earns trust. There are seven divisors.
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 “Allowed exponents are 0,1,2,3,4,5,6.” from memory, but to recreate a justified answer from the new evidence.
Practice 12: Proof
Question. Why are there no other forms?
Explained answer. Seven is prime.
Why this earns trust. The count product has one factor only.
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 “Seven is prime.” from memory, but to recreate a justified answer from the new evidence.
Practice 13: Pairing
Question. Why can the count be odd?
Explained answer. p⁶ is a square with one self-paired middle factor.
Why this earns trust. Factor pairs are reconciled.
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 “p⁶ is a square with one self-paired middle factor.” from memory, but to recreate a justified answer from the new evidence.
Practice 14: Routine
Question. State the method.
Explained answer. Prime-factorise, count choices, solve, verify.
Why this earns trust. The method generalises.
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 “Prime-factorise, count choices, solve, 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. The 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 original reasoning.
Transfer test 4: Blank recall
Rebuild the idea after one week.
Success criterion. Definition, example, near-miss and boundary appear.
Examination control
1. Factor completely. Composite bases must be rewritten with prime bases.
2. Translate exactly into an equation. Set the divisor-count product equal to seven.
3. Use the prime target. Seven permits only one choice factor.
4. Subtract one. Seven choices means exponent six.
5. Prove the converse. Show p⁰ through p⁶.
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 error by the failed decision rather than writing “careless”. A precise 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 the controlling evidence before accepting the answer.
Let the learner attempt a near-miss before explaining the rule again.
Praise precise limits and checks, not speed alone.
Use fresh contexts so the learner transfers the decision rather than memorising one example.
Frequently asked questions
What form has seven factors?
p⁶ for prime p.
Why exponent six?
It creates seven exponent choices.
Can the base be composite?
No.
Why not two primes?
Their choice counts would form a product, but seven is prime.
What is the smallest example?
64.
Is 128 valid?
No, it has eight factors.
Why is the count odd?
The number is a square with one self-paired factor.
What is the general count rule?
Multiply one more than each 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.