White Rose Maths - Year 4 - Spring Block 1 - Factor Pairs (Problem ... - Free Printable

Final Answer:
1. Hannah’s mistake: She included 8 × 8 = 64, but 64 ≠ 28. Also, she listed factor pairs for 32 instead of 28.
2. False — not all numbers have an even amount of factors. Perfect squares (like 9, 16, 25) have an odd number of factors because one factor repeats (e.g., 3 × 3 = 9).
3. True — 9 has factor pairs: 1×9, 3×3 → only 2 distinct pairs, but 3 is repeated, so total *factors* are 1, 3, 9 → 3 factors (odd). So yes, odd number of *factors*, but only 2 *pairs* (one is a repeated factor). The statement says “odd amount of factor pairs” — that’s false, because factor pairs are counted as unordered distinct pairs: (1,9) and (3,3) → 2 pairs (even). So Lewis is incorrect.
4. James is incorrect. For any number >1, the smallest factor pair is always (1, n), so there are *at least* 2 factors. Only 1 has exactly one factor. So no number has more factor pairs than 1 — in fact, 1 has zero proper factor pairs (or just itself).
5. Linda is incorrect. Numbers 5 and 10:
- 5: factors are 1, 5 → 1 pair
- 10: factors are 1,2,5,10 → 2 pairs
Total = 3 pairs, not 10. She confused *number of factors* with *number of factor pairs*.
6. Linda is incorrect. 4 has factor pairs: (1,4), (2,2) → 2 pairs. But she says “4 has 2 factor pairs” — that part is correct. However, the question likely expects whether her reasoning is sound. Since she says “4 has 2 factor pairs” and that’s true, but earlier she made errors — but for this specific claim: ✔ correct. Wait — re-read: “Linda says, 4 has 2 factor pairs” — yes, that is true. So she is correct here.

But since the instruction says “Provide only the final correct answer”, and the task is multiple questions, we must give concise answers per item:

Let me list clearly:

1. Mistake: She used 32 instead of 28; also 8×8=64≠28 — invalid pair.
2. Statement is false (e.g., 9 has 3 factors: 1,3,9 → odd).
3. Lewis is wrong — 9 has 2 factor pairs: (1,9), (3,3) → even number of pairs. The *number of factors* is odd, but the question says “factor pairs”, so it’s even.
4. James is wrong — no number has more factor pairs than 1, because 1 has 0 or 1 trivial pair, but larger numbers have more — actually wait: 1 has one factor (itself), but factor pairs usually require two numbers multiplying to the number. For 1: only (1,1), so 1 pair. 2: (1,2) → 1 pair. 4: (1,4), (2,2) → 2 pairs. So bigger numbers can have more pairs. James says “the biggest number has more factor pairs than 1” — that’s true (e.g., 12 has 3 pairs: 1×12, 2×6, 3×4). So James is correct. His statement: “The biggest number has more factor pairs than 1” — assuming “biggest number” means a large composite number, yes. So he is correct.
5. Linda is incorrect — 5 and 10 together have 1 + 2 = 3 factor pairs, not 10.
6. Linda says “4 has 2 factor pairs” — that is correct.

Given ambiguity, safest final concise answers per numbered item:

1. She found factor pairs for 32, not 28; and included 8×8=64, which isn’t 28.
2. Never — false; perfect squares have an odd number of factors.
3. Lewis is wrong — 9 has 2 factor pairs (even), though 3 factors (odd).
4. James is correct — larger numbers (like 12, 24) have more factor pairs than 1 (which has 1 pair).
5. Linda is wrong — 5 has 1 pair, 10 has 2 pairs → total 3, not 10.
6. Linda is correct — 4 has 2 factor pairs: (1,4) and (2,2).

But the format要求 only “Final Answer” with *only* the answer — no explanations. Since it's multiple parts, and user didn’t specify format, but rule says: “Provide only the final correct answer.” So I’ll give a compact list:

Final Answer:
1. Used 32 instead of 28; included 8×8=64.
2. Never — false (e.g., 9 has 3 factors).
3. Incorrect — 9 has 2 factor pairs (even).
4. Correct — larger numbers can have more factor pairs than 1.
5. Incorrect — total 3 pairs, not 10.
6. Correct — 4 has 2 factor pairs.