Factors and multiples
Objective. List factor pairs and identify common multiples.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A factor of a number divides into it exactly, while a multiple is what you get by multiplying a number by a whole number. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12, because each divides 12 with no remainder. To list factors systematically, pair them up from the outside in: 1×12, 2×6, 3×4. Multiples of 7 are 7, 14, 21, 28 and so on, stretching forever. A common multiple of two numbers, such as 6 and 8, appears in both lists — 24 is the smallest one. Checking a factor pair by multiplying it back is the surest way to avoid missing one.
Worked example
List all the factors of 18 and state its smallest common multiple with 12.
- 1Find factor pairs of 18: 1×18, 2×9, 3×6.
- 2List the factors in order: 1, 2, 3, 6, 9, 18.
- 3List multiples of 18 and 12 until one matches: 18, 36; 12, 24, 36.
- 4The smallest common multiple is 36.
Answer: Factors of 18: 1, 2, 3, 6, 9, 18; smallest common multiple with 12 is 36
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Practice
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Start practisingCommon mistake. Pupils often confuse factors with multiples, saying the factors of 5 are 5, 10, 15. Remind them factors are always less than or equal to the number, while multiples grow larger than it, by testing with division.
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