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 notices that sixteen is a power of two but lists only p¹⁵, missing four other exponent structures created by the multiplicative partitions of sixteen. 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
A number has exactly sixteen positive factors when the product of its prime-exponent choice counts equals 16. Because 16 has several multiplicative partitions, several structures are possible.
For n=pᵃqᵇ…, the divisor count is (a+1)(b+1)… after the number is written with distinct prime bases.
The complete unordered multiplicative partitions of 16 into integers greater than one are 16, 8×2, 4×4, 4×2×2 and 2×2×2×2.
Subtracting one from each choice factor gives exponent patterns 15; 7,1; 3,3; 3,1,1; and 1,1,1,1.
Therefore the five forms are p¹⁵, p⁷q, p³q³, p³qr and pqrs, with all displayed prime letters distinct within a form.
Order does not create additional families. For example, p⁷q and pq⁷ share the same exponent pattern after the prime names are exchanged.
The mixed prime bases must be distinct. If two letters name the same prime, their exponents combine and the factor count changes.
The four-prime square-free form pqrs has 2⁴=16 divisors because every prime is either included or excluded from a divisor.
The p³q³ form has 4×4=16 choices, while p³qr has 4×2×2=16. Similar-looking expressions can belong to different partitions.
Examples confirm a form but cannot prove that the list is complete. Completeness comes from listing every multiplicative partition of 16.
Some qualifying numbers are squares and some are not. The one-factor p¹⁵ form has an odd exponent, and pqrs is square-free, so no single perfect-power label describes every case.
The reliable routine is factor canonically, write the choice product, list all five partitions, subtract one, enforce distinct primes and verify each form.
Core decision: Exactly sixteen positive factors occurs in five forms: p¹⁵, p⁷q, p³q³, p³qr and pqrs, with distinct prime bases as shown. These correspond to 16, 8×2, 4×4, 4×2×2 and 2×2×2×2.
Divisor classification is multiplicative partitioning. Every present prime supplies at least two exponent choices, so the target’s factorisations determine both the number of prime bases and their exponents.
Mechanism: why the rule works
1. Factor canonically
Use distinct prime bases and combine repeated ones.
Only canonical exponents create independent divisor choices.
Diagnostic check. Are all bases prime and distinct?
2. Build the choice product
Replace each exponent a with a+1.
Zero through a gives a+1 choices.
Diagnostic check. What product must equal sixteen?
3. List partitions
Write 16; 8×2; 4×4; 4×2×2; 2×2×2×2.
This is the completeness engine.
Diagnostic check. Has any unordered partition been omitted?
4. Translate exponents
Subtract one from every partition factor.
Choice counts become prime exponents.
Diagnostic check. Were all factors converted?
5. Enforce distinctness
Different letters must be different primes.
Equal bases combine and alter the pattern.
Diagnostic check. Are like primes combined first?
6. Remove duplicate orders
Renaming primes does not create a new family.
Classify exponent multisets rather than letter order.
Diagnostic check. Is this merely a permutation?
7. Verify each form
Multiply exponent-plus-one values.
Every valid form must return sixteen.
Diagnostic check. Does the proposed form pass the formula?
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: One base
Task. 2¹⁵ has exponent choices 0 through 15.
Reasoning. There are sixteen choices.
Answer. It qualifies as p¹⁵.
Independent check. Do not use exponent 16.
Contrast-and-transfer pass. Keep the governing principle from “One base”, but change one surface detail in the task: 2¹⁵ has exponent choices 0 through 15. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It qualifies as p¹⁵.—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: Eight by two
Task. 2⁷×3 has 8×2 choices.
Reasoning. The product is sixteen.
Answer. It fits p⁷q.
Independent check. The primes are distinct.
Contrast-and-transfer pass. Keep the governing principle from “Eight by two”, but change one surface detail in the task: 2⁷×3 has 8×2 choices. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It fits p⁷q.—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: Four by four
Task. 2³×3³ has 4×4 choices.
Reasoning. The product is sixteen.
Answer. It fits p³q³.
Independent check. Equal exponents are allowed on distinct bases.
Contrast-and-transfer pass. Keep the governing principle from “Four by four”, but change one surface detail in the task: 2³×3³ has 4×4 choices. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It fits p³q³.—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: Four by two by two
Task. 2³×3×5 has 4×2×2 choices.
Reasoning. The product is sixteen.
Answer. It fits p³qr.
Independent check. Three bases appear.
Contrast-and-transfer pass. Keep the governing principle from “Four by two by two”, but change one surface detail in the task: 2³×3×5 has 4×2×2 choices. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It fits p³qr.—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 linear primes
Task. 2×3×5×7 has 2⁴ choices.
Reasoning. The product is sixteen.
Answer. It fits pqrs.
Independent check. Every divisor chooses include or exclude.
Contrast-and-transfer pass. Keep the governing principle from “Four linear primes”, but change one surface detail in the task: 2×3×5×7 has 2⁴ choices. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It fits pqrs.—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: Wrong p¹⁶
Task. p¹⁶ has seventeen factors.
Reasoning. Choices run from 0 through 16.
Answer. It does not qualify.
Independent check. Subtract one.
Contrast-and-transfer pass. Keep the governing principle from “Wrong p¹⁶”, but change one surface detail in the task: p¹⁶ has seventeen factors. 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: Repeated-base error
Task. p³×p×q=p⁴q.
Reasoning. The choice product is 5×2=10.
Answer. It does not fit p³qr.
Independent check. Prime letters must be distinct.
Contrast-and-transfer pass. Keep the governing principle from “Repeated-base error”, but change one surface detail in the task: p³×p×q=p⁴q. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It does not fit p³qr.—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: Permutation
Task. p q⁷ has exponents 1 and 7.
Reasoning. Rename q as p and p as q.
Answer. It is the p⁷q family.
Independent check. Do not double-count.
Contrast-and-transfer pass. Keep the governing principle from “Permutation”, but change one surface detail in the task: p q⁷ has exponents 1 and 7. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—It is the p⁷q family.—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: Candidate 216
Task. 216=2³×3³.
Reasoning. The choice product is 4×4.
Answer. 216 has sixteen factors.
Independent check. It matches the equal-cubes form.
Contrast-and-transfer pass. Keep the governing principle from “Candidate 216”, but change one surface detail in the task: 216=2³×3³. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—216 has sixteen 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: Candidate 210
Task. 210=2×3×5×7.
Reasoning. The choice product is 2⁴.
Answer. 210 has sixteen factors.
Independent check. It is square-free.
Contrast-and-transfer pass. Keep the governing principle from “Candidate 210”, but change one surface detail in the task: 210=2×3×5×7. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—210 has sixteen 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 11: Candidate 144
Task. 144=2⁴×3².
Reasoning. The count is 5×3=15.
Answer. It does not qualify.
Independent check. Nearby target structures must not be mixed.
Contrast-and-transfer pass. Keep the governing principle from “Candidate 144”, 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 12: Completeness
Task. Could exponents 5 and 1 work?
Reasoning. They give 6×2=12.
Answer. No.
Independent check. Only partitions of sixteen qualify.
Contrast-and-transfer pass. Keep the governing principle from “Completeness”, but change one surface detail in the task: Could exponents 5 and 1 work? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—No.—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 three controlled cases around this problem: the learner notices that sixteen is a power of two but lists only p¹⁵, missing four other exponent structures created by the multiplicative partitions of sixteen. Include one valid example, one near-miss and one boundary case. Change only one decisive condition at a time and name the evidence that changes the decision.
Turn the central claim into a decision card: Exactly sixteen positive factors occurs in five forms: p¹⁵, p⁷q, p³q³, p³qr and pqrs, with distinct prime bases as shown. These correspond to 16, 8×2, 4×4, 4×2×2 and 2×2×2×2. Put the trigger on the front. On the back, write the mechanism, one worked example, one tempting wrong answer and the limit.
Make an evidence ladder with four rungs: given information or observation, interpreted relationship, conclusion and independent check. Rewrite any rung that merely repeats another.
Construct two attractive 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.
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…”.
After two days, attempt one direct item, one disguised item and one item where the rule should not be used. After one week, rebuild the rule on a blank page and verify it independently.
Common misconceptions and targeted repairs
Misconception 1: Only p¹⁵
What the learner may think. Sixteen factors means one structure.
Why it fails. Composite target counts have several partitions.
Targeted repair. List them first.
Misconception 2: Use p¹⁶
What the learner may think. Target equals exponent.
Why it fails. Exponent plus one equals choices.
Targeted repair. Subtract one.
Misconception 3: Omit four primes
What the learner may think. Too many prime bases cannot fit.
Why it fails. 2×2×2×2=16 fits exactly.
Targeted repair. Use minimum choice factors.
Misconception 4: Treat order as new
What the learner may think. p⁷q and pq⁷ are separate.
Why it fails. They are prime-name permutations.
Targeted repair. Use exponent patterns.
Misconception 5: Allow equal letters
What the learner may think. p, q, r may name the same prime.
Why it fails. Repeated bases combine.
Targeted repair. Require distinct primes.
Misconception 6: Add counts
What the learner may think. Choice factors should be added.
Why it fails. Independent choices multiply.
Targeted repair. Use a grid or product.
Misconception 7: Examples complete proof
What the learner may think. Five examples prove no other forms.
Why it fails. Only complete partitioning proves that.
Targeted repair. Show the partitions.
Misconception 8: All are squares
What the learner may think. Sixteen is a square, so all qualifying numbers are squares.
Why it fails. Several forms have odd exponents.
Targeted repair. Inspect each structure.
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: Count
Question. How many structures are there?
Explained answer. Five.
Why this earns trust. They come from five partitions.
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.” from memory, but to recreate a justified answer from the new evidence.
Practice 2: Partitions
Question. List them.
Explained answer. 16; 8×2; 4×4; 4×2×2; 2×2×2×2.
Why this earns trust. Order is ignored.
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 “16; 8×2; 4×4; 4×2×2; 2×2×2×2.” from memory, but to recreate a justified answer from the new evidence.
Practice 3: Forms
Question. List the exponent forms.
Explained answer. p¹⁵, p⁷q, p³q³, p³qr and pqrs.
Why this earns trust. Primes are distinct as shown.
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 “p¹⁵, p⁷q, p³q³, p³qr and pqrs.” from memory, but to recreate a justified answer from the new evidence.
Practice 4: One base
Question. Why exponent fifteen?
Explained answer. Sixteen choices run from zero to fifteen.
Why this earns trust. Subtract one.
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 “Sixteen choices run from zero to fifteen.” from memory, but to recreate a justified answer from the new evidence.
Practice 5: Four primes
Question. Why does pqrs have sixteen factors?
Explained answer. Each prime has include-or-exclude choices, giving 2⁴.
Why this earns trust. The number is square-free.
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 “Each prime has include-or-exclude choices, giving 2⁴.” from memory, but to recreate a justified answer from the new evidence.
Practice 6: Check 216
Question. Does 216 qualify?
Explained answer. Yes, 216=2³×3³.
Why this earns trust. 4×4=16.
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, 216=2³×3³.” from memory, but to recreate a justified answer from the new evidence.
Practice 7: Check 210
Question. Does 210 qualify?
Explained answer. Yes, 210=2×3×5×7.
Why this earns trust. 2⁴=16.
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, 210=2×3×5×7.” from memory, but to recreate a justified answer from the new evidence.
Practice 8: Check p¹⁶
Question. Does it qualify?
Explained answer. No, it has seventeen factors.
Why this earns trust. Include exponent zero.
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 seventeen factors.” from memory, but to recreate a justified answer from the new evidence.
Practice 9: Distinctness
Question. Why must letters be distinct?
Explained answer. Equal prime bases combine.
Why this earns trust. The exponent pattern changes.
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 “Equal prime bases combine.” from memory, but to recreate a justified answer from the new evidence.
Practice 10: Permutation
Question. Is p q⁷ new?
Explained answer. No.
Why this earns trust. Rename primes.
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: Square
Question. Are all qualifying numbers squares?
Explained answer. No.
Why this earns trust. Several forms have odd exponents.
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 12: Formula
Question. State the divisor formula.
Explained answer. Multiply one more than each prime exponent.
Why this earns trust. Use canonical factorisation.
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 “Multiply one more than each prime exponent.” from memory, but to recreate a justified answer from the new evidence.
Practice 13: Completeness
Question. What proves the list complete?
Explained answer. The complete multiplicative partitions of sixteen.
Why this earns trust. Examples alone do not.
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 “The complete multiplicative partitions of sixteen.” from memory, but to recreate a justified answer from the new evidence.
Practice 14: Routine
Question. State the method.
Explained answer. Factor, form choices, partition 16, subtract one, check distinctness and verify.
Why this earns trust. Every gate is explicit.
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, form choices, partition 16, subtract one, check distinctness 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. The trigger, mechanism and limit are all 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 the conclusion by a second route.
Success criterion. The check does not repeat the same possible mistake.
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. Combine like primes.
2. Write the choice product. Use exponent plus one.
3. List all five partitions. Completeness matters.
4. Remove permutations. Do not double-count forms.
5. Verify distinct primes. Protect the choice structure.
Under time pressure, compress the method to choice product 16 → five partitions → subtract one → distinct-prime verification. 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 five forms?
p¹⁵, p⁷q, p³q³, p³qr and pqrs.
Why five?
Sixteen has five unordered multiplicative partitions above one.
Must primes be distinct?
Yes, where different letters appear.
Does p¹⁶ work?
No.
Does pqrs work?
Yes.
Is p q⁷ a new form?
No.
Are all qualifying numbers squares?
No.
What proves completeness?
Listing every multiplicative partition of sixteen.
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.