Higher November 2024 Paper 1 Q6
6
\[\begin{aligned} A &= 2^3 \times 5^4 \times 7 \times 11 \\ B &= 2^2 \times 5^2 \times 7^2 \\ C &= 2^2 \times 5^3 \times 7^4 \end{aligned}\]Find the highest common factor (HCF) of \(A\), \(B\) and \(C\)
Write your answer as a product of prime factors.
(2)
| Scheme | Marks |
|---|---|
| B1 for \(2^2 \times 5^2\) oe or \(2 \times 2 \times 5 \times 5\) oe or \(2^2 \times 7\) oe or \(2 \times 2 \times 7\) oe or \(5^2 \times 7\) oe or \(5 \times 5 \times 7\) oe or \(2^2 \times 5 \times 7\) oe or \(2 \times 2 \times 5 \times 7\) oe or \(2 \times 5^2 \times 7\) oe or \(2 \times 5 \times 5 \times 7\) oe or \(2^2 \times 5^2 \times 7 \times 11\) or \(2 \times 2 \times 5 \times 5 \times 7 \times 11\) oe or 700 or \(2^p \times 5^q \times 7^r\) where two of \(p\) or \(q\) or \(r\) are correct Answer: \(2^2 \times 5^2 \times 7\) | B2 |
| (2) | |
| (2 marks) |
Notes
B2: Allow \(2 \times 2 \times 5 \times 5 \times 7\)
Answers must be a product of prime factors
Can be in any order (allow \(2^2 \,.\, 5^2 \,.\, 7\))
Do not allow 1 in the final answer
\(2 \times 2 \times 5 \times 5 \times 7\) in working space and 700 on answer line award B2
\(2^2 \times 5^2 \times 7\) in working space and 700 on answer line award B2
(B1 for \(2^p \times 5^q \times 7^r\) where two of \(p\) or \(q\) or \(r\) are correct
or
one mistake in their product
(see working on the left for examples)
or
for 700)