4MA0 Higher January 2015 Paper 3 Q11
11
\(3780 = 2^2 \times 3^3 \times 5 \times 7\)
\(3240 = 2^3 \times 3^4 \times 5\)
(a) Find the highest common factor (HCF) of 3780 and 3240
Give your answer as a product of prime factors. (2)
Give your answer as a product of prime factors. (2)
(b) Find the lowest common multiple (LCM) of 3780 and 3240
Give your answer as a product of prime factors. (2)
Give your answer as a product of prime factors. (2)
| Scheme | Marks |
|---|---|
| M1 | |
| \(2 \times 2 \times 3 \times 3 \times 3 \times 5\) | A1 |
| (2) |
Notes
M1: For identifying \(2^2\), \(3^3\), and 5 or
any product of integer powers of 2 and 3 and 5 where at least two powers are correct and the third is greater than 0 or
540
A1: Accept \(2^2 \times 3^3 \times 5\)
| Scheme | Marks |
|---|---|
| M1 | |
| \(2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \times 7\) | A1 |
| (2) | |
| (4 marks) |
Notes
M1: For identifying \(2^3\), \(3^4\), 5 and 7 or any product of integer powers of 2 and 3 and 5 and 7, where at least three powers are correct and the fourth is greater than 0.
Accept a product that includes 2, 3 and 5 and 7 and multiplies to 22680 (Eg \(2^3 \times 3^2 \times 5 \times 7 \times 9\)) or 22680
A1: Accept \(2^3 \times 3^4 \times 5 \times 7\)