0580.C1.1.06 — Identify and use: find the highest common factor (HCF) of two.: past paper questions

Real questions on 0580.c1.1.06 — identify and use: find the highest common factor (hcf) of two.

The newest 20 of 33 written questions. Open one to see it on the real paper.

1. 0580/13 · May/June 2026 · Q19b[1]
   (b) 96 can be written as $2^P\times 3$. Find the value of $P$.See it on the paper →
2. 0580/21 · May/June 2026 · Q10a[1]
   10 (a) $24192=2^7\times 3^3\times 7$ $245000=2^3\times 5^4\times 7^2$ Find the highest common factor (HCF) of 24 192 and 245 000.See it on the paper →
3. 0580/22 · May/June 2026 · Q7[2]
   7 Factorise. $6wx-4xy$See it on the paper →
4. 0580/22 · May/June 2026 · Q9c[2]
   (c) Find the highest common factor (HCF) of $63a^5{c}^2$ and $42a^2{c}^5$.See it on the paper →
5. 0580/23 · May/June 2026 · Q22b[2]
   (b) $16^n=64$ Find the value of $n$. $n=$See it on the paper →
6. 0580/32 · May/June 2026 · Q2b[2]
   (b) Write down all the common factors of 20 and 30.See it on the paper →
7. 0580/32 · May/June 2026 · Q22[2]
   22 Find the lowest common multiple (LCM) of 54 and 90.See it on the paper →
8. 0580/12 · February/March 2026 · Q9a[2]
   9 (a) Work out the difference between $5^2$ and $2^3$.See it on the paper →
9. 0580/01 · Specimen 2025 · Q3[12]

   12-mark “Find” question — its maths and diagrams are best seen on the paper.

   See it on the paper →
10. 0580/03 · Specimen 2025 · Q17b[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
11. 0580/12 · October/November 2025 · Q4b[1]
    (b) Work out the value of $5^3$.See it on the paper →
12. 0580/13 · October/November 2025 · Q9a[1]
    9 Find the value of (a) $2^5$See it on the paper →
13. 0580/13 · October/November 2025 · Q9b[1]
    9 Find the value of (b) $6^0$.See it on the paper →
14. 0580/23 · October/November 2025 · Q2[1]
    2 Find the largest **odd** number that is a common factor of 90 and 120.See it on the paper →
15. 0580/11 · May/June 2025 · Q22a[1]
    22 $A=2^3\times 3$ $B=3^2\times 5$ (a) Find the highest common factor (HCF) of $A$ and $B$.See it on the paper →
16. 0580/13 · May/June 2025 · Q20[2]
    20 Find the highest common factor (HCF) of 36 and 54.See it on the paper →
17. 0580/22 · May/June 2025 · Q8[2]
    8 Find the highest common factor (HCF) of 36 and 54.See it on the paper →
18. 0580/23 · May/June 2025 · Q8b[2]
    (b) Find the highest common factor (HCF) of 84 and 70.See it on the paper →
19. 0580/11 · May/June 2024 · Q18[2]
    18 Find the greatest **odd** number that is a factor of 140 and a factor of 210.See it on the paper →
20. 0580/21 · May/June 2024 · Q4[2]
    4 Find the greatest **odd** number that is a factor of 140 and a factor of 210.See it on the paper →

What examiners said

Comprehensive responses • Many candidates worked out the squaring and cubing correctly and most understood that they then had to subtract these. Limited responses • Some candidates did not find the difference as required, or were unclear about its meaning. • Those not understanding indices usually gave responses of 10 and 6 leading to an answer of 4.

— Examiner report, February/March 2026, 0580/12 Q9(a) (Cambridge)

Most candidates attempted this question with less than half having a correct response. Some seemed to think that 23 and 32 were the same value so gave an answer of 6. Many worked out the values of A and B, i.e., 24 and 45. Some gave the LCM or another multiple.

— Examiner report, May/June 2025, 0580/11 Q22(a) (Cambridge)

Around half the candidates scored full marks on this question, common errors included miscalculations, or having correct factor trees but then multiplying all the factors, confusing HCF and LCM. Some left their answer in the form 2 3 3 without simplifying. Others scored zero for multiplying 36 by 54.

— Examiner report, May/June 2025, 0580/13 Q20 (Cambridge)