Number 3

4 marks · Normal

Express 150 as a product of its prime factors. Use your answer to find the highest common factor (HCF) of 150 and 180.

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150 = 2 × 3 × 5^2; HCF(150,180) = 30

Also accept: 150 = 2 × 3 × 5^2 and 180 = 2^2 × 3^2 × 5; HCF = 2 × 3 × 5 = 30; HCF = 30

Common mistakes: Wrong prime factors; LCM instead of HCF

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Marking points

M1 · 1 mark · Begins prime factorisation for 150.

A1 · 1 mark · Correct product of prime factors for 150.

M2 · 1 mark · States correct product of prime factors for 180.

A2 · 1 mark · Identifies all common primes and finds HCF correctly. (follow-through)

Worked solution

150 = 2 × 75 = 2 × 3 × 25 = 2 × 3 × 5 × 5 = 2 × 3 × 5^2

180 = 2 × 90 = 2 × 2 × 45 = 2^2 × 3 × 15 = 2^2 × 3 × 3 × 5 = 2^2 × 3^2 × 5

Common primes: one 2, one 3, one 5