Foundation January 2023 Paper 2R Q21
21
(a) Find the highest common factor (HCF) of 200 and 420 (2)
\(A = 2^3 \times 3 \times 5 \times 7^2\)
\(B = 2 \times 3^2 \times 7\)
\(C = 3 \times 5^2 \times 11\)
(b) Find the lowest common multiple (LCM) of \(A\), \(B\) and \(C\)
Write your answer as a product of powers of prime factors. (2)
Write your answer as a product of powers of prime factors. (2)
| Scheme | Marks | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 × 2 × 2 × 5 × 5 or 2, 2, 2, 5, 5 or 2 × 2 × 3 × 5 × 7 or 2, 2, 3, 5, 7 or eg
| M1 | ||||||||||||
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 20 | A1 | ||||||||||||
| (2) |
Notes
M1: for one number written as a product of prime factors or prime factors listed – numbers may be at end of factor trees or on ‘ladder diagrams’ or in a table or in a Venn diagram
or
at least two factors for each (excluding 1, 200, 420)
A1: or \(2^2 \times 5\) oe
| Scheme | Marks |
|---|---|
 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(2^3 \times 3^2 \times 5^2 \times 7^2 \times 11\) | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for \(2^m \times 3^n \times 5^p \times 7^q \times 11^r\) with at least three of \(m = 3\), \(n = 2\), \(p = 2\), \(q = 2\), \(r = 1\) (all 5 terms should be seen) or omission of one term with others fully correct
OR prime factors seen in a Venn diagram – if so must be fully correct
A1: allow 970 200 oe