1MA0 Higher November 2014 Paper 1 Q13
13
(a) Express 180 as a product of its prime factors. (3)
Martin thinks of two numbers.
He says,
“The Highest Common Factor (HCF) of my two numbers is 6
The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15”
(b) Write down two possible numbers that Martin is thinking of. (2)
| Answer | Mark | Notes |
|---|---|---|
| \(2 \times 2 \times 3 \times 3 \times 5\) | 3 | M1 for a continual prime factorisation (at least two consecutive steps correct) or at least two stages of a factor tree correct M1 for a fully correct factor tree or list 2,2,3,3,5 A1 for \(2 \times 2 \times 3 \times 3 \times 5\) or \(2^2 \times 3^2 \times 5\) |
| Answer | Mark | Notes |
|---|---|---|
| Eg 6, 30 | 2 | M1 for two numbers with an HCF of 6 or for two numbers with a LCM a multiple of 15 A1 for two numbers with an HCF of 6 and a LCM a multiple of 15 (eg (6, 30), (12, 30), …) OR M1 for \(2 \times 3\) and \(3 \times 5\) or for \(2 \times 3 \times 5\) A1 for two numbers with an HCF of 6 and a LCM a multiple of 15 eg (6, 30) (12, 30) … |