Number 3

3 marks · Normal

A school has 96 red pens and 120 blue pens. Each box packed must have the same number of red pens and the same number of blue pens, with none left over. What is the greatest number of boxes that can be packed?

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24 (±0)

Also accept: HCF of 96 and 120 = 24; 24

Common mistakes: Taking LCM instead of HCF

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Marking points

M1 · 1 mark · Begins dividing both quantities into factors or describes method for HCF.

M2 · 1 mark · Finds all factors of both numbers.

A1 · 1 mark · States final correct HCF: 24. (follow-through)

Worked solution

Prime factors:

96 = 2^5 × 3, 120 = 2^3 × 3 × 5

Common prime factors: 2^3 × 3

Greatest number of boxes is 24.