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Factors and multiples
AQA GCSE Mathematics practice questions with step-by-step solutions
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EasyQuestion 1
[2 marks](a) List all the factors of 18.
(b) Write down the first five multiples of 7.
Solution for Question 1
MediumQuestion 2
[3 marks]A number has exactly four factors: 1, 2, 4, and itself.
What is the number?
Solution for Question 2
HardQuestion 3
[3 marks]Find the smallest number that is:
- a multiple of 6
- a factor of 180
- greater than 20
Solution for Question 3
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Generate Unlimited QuestionsAbout Factors and multiples in AQA GCSE
Factors are numbers that divide exactly into another number. Multiples are numbers in a times table. For example, factors of 12 are 1, 2, 3, 4, 6, 12, while multiples of 12 are 12, 24, 36, 48...
To find all factors of a number systematically, start with 1 and work up, testing each number. Factors come in pairs that multiply to give your number. For 24: 1×24, 2×12, 3×8, 4×6, so factors are 1, 2, 3, 4, 6, 8, 12, 24.
A quick check: every number has 1 and itself as factors. Even numbers always have 2 as a factor. Numbers ending in 0 or 5 have 5 as a factor. The digit sum rule works for 3 and 9: if digits sum to a multiple of 3 (or 9), the number is divisible by 3 (or 9).
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