Working required Answer: \(2^3 \times 5^2 \times 7\)
A1
(3)
(3 marks)
Notes
M1: for finding 2 prime factors after at least 2 stages of prime factorisation with 0 incorrect stages or for finding 2 prime factors after at least 3 stages of prime factorisation with no more than 1 incorrect stage
Each stage gives 2 factors – may be in a factor tree or a table or listed (see LHS for examples of the amount of work needed for the award of this mark) but we want to see 2 prime factors.
Example of finding 2 prime factors after at least 3 stages with 1 incorrect stage: 1400 = 10 × 14 = 2 × 5 × 2 × 7
M1: dep on M1 for factors 2, 2, 2, 5, 5, 7 identified with no others in any form, eg listed, multiplied, added
Ignore 1s
May be seen in a fully correct factor tree or ladder
A1: dep on M2 May be in any order and allow \(2^3 \text{x} 5^2 \text{x} 7\)
\[\begin{aligned} A &= 2^3 \times 5^4 \times 7 \times 11 \\ B &= 2^2 \times 5^2 \times 7^2 \\ C &= 2^2 \times 5^3 \times 7^4 \end{aligned}\]
Find the highest common factor (HCF) of \(A\), \(B\) and \(C\) Write your answer as a product of prime factors.
(2)
Mark scheme
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)
