Foundation January 2019 Paper 2 Q20
20
(a) Find the highest common factor (HCF) of 96 and 120 (2)
\(A = 2^3 \times 5 \times 7^2 \times 11\)
\(B = 2^4 \times 7 \times 11\)
\(C = 3 \times 5^2\)
(b) Find the lowest common multiple (LCM) of \(A\), \(B\) and \(C\). (2)
| Scheme | Marks | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 × 2 × 2 × 2 × 2 × 3 or 2 × 2 × 2 × 3 × 5 e.g.
| M1 | ||||||||||||||||||||||||
| 24 | A1 | ||||||||||||||||||||||||
| (2) |
Notes
M1: for one number written as product of prime factors number may be at the end of factor trees or on ‘ladder diagrams’
or
Use of table method (allow 1 error), 2 examples shown but could have 2, 3, 4, 6, 12, 24 along the side
or
at least 2 factors for each (excluding 1, 96, 120)
A1: or \(2^3 \times 3\)
| Scheme | Marks |
|---|---|
| M1 | |
| 646 800 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for \(2^m \times 3^n \times 5^p \times 7^q \times 11^r\) with at least two of \(m = 4\), \(n = 1\), \(p = 2\), \(q = 2\), \(r = 1\) (or omission of one with others fully correct)
or prime numbers may be seen in a Venn diagram – if so must be correctly placed
A1: or \(2^4 \times 3 \times 5^2 \times 7^2 \times 11\) oe