Mathematics · May / June 2026 · Paper 22 · Question 9

3 × 3 × 7 or 32 × 7[1] [2]

B1 for 3, 3, 7 Allow

B1 for the inclusion of 1 with correct factors.

or M1 for correct factor tree/diagram/list/table

126 [2]

B1 for 126k as final answer, where B1 evaluated e.g. 252, 378, 504, 630, 756, 882, k is an integer 1008, 1134, 1260, 1386, 1512, 1638, 1764, 1890, 2016, 2142, 2268 etc.

or M1 for [42 =] 2 × 3 × 7 For M mark allow inclusion of 1 but do not allow 2 × 21. Allow prime factors of 42 not as a product, e.g. in a factor tree/diagram/list/table or for 2 × 3 × 3 × 7 oe When combining the prime factors, allow 21 for 3 × 7 and allow picking out of correct combined tables/diagrams for M1, e.g. 63 42 3 63 42 21 21 14 7 3 2 3 2

21a2c2 [2]

B1 for answers ka2c2 or 21amcn or k can be any value or numerical product. 3, 7, a2, c2 m and n can be any values e.g.

B1 for 21 alone. or for 21a2c2 seen then spoilt Also allow answer 21, a2, c2 for B1.