Factors and multiples · Usually met around P4
Factors
Find them in pairs; stop when the pair meets.
How to do it
Method
Find them in pairs; stop when the pair meets
36 = 1 × 36 = 2 × 18 = 3 × 12 = 4 × 9 = 6 × 6
Another way
Divide in turn
36 ÷ 1, 2, 3, 4, 6, 9, 12, 18, 36 all divide exactly
In full
Every number that divides a number exactly is a factor of it. To find all the factors of 36, find them in pairs: try from 1 up, 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6, and stop when the two meet (or would swap). So 36's factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36: 9 of them. 1 and the number itself are always factors, and the largest factor is the number itself. The pair 6 × 6 gives only one 6, so a square number has an odd number of factors. Or divide by 1, 2, 3… in turn and keep those that divide exactly: the same answer. 4 is a factor of 36, which is to say 36 is a multiple of 4.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Finding the factors of 48 in pairs: 1 × 48, 2 × □, 3 × □, 4 × □, …
Fill in each box
Show the answer and working
Answer: 24，16，12
48 ÷ 2 = 24, 48 ÷ 3 = 16, 48 ÷ 4 = 12: each pair multiplies to 48.
Example 2
How many factors does 72 have?
Show the answer and working
Answer: 12
Find the factors of 72 in pairs from 1 until the pair meets: 12 in all.
Example 3
24 ÷ 6 = 4 with no remainder. Which sentence is true?
- A. 4 is a multiple of 6
- B. 6 is a multiple of 24
- C. 6 is a factor of 24
- D. 24 is a factor of 6
Choose the right answer
Show the answer and working
Answer: C. 6 is a factor of 24
6 divides 24 exactly, so 6 is a factor of 24 and 24 is a multiple of 6.
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