Factors and multiples · Usually met around P4
Common factors and common multiples
List both and ring what's in both.
How to do it
Method
List both and ring what's in both
12: 1, 2, 3, 4, 6, 12; 18: 1, 2, 3, 6, 9, 18 → 1, 2, 3, 6
Another way
Start from the H.C.F.
The H.C.F. is 6; its factors 1, 2, 3, 6 are the common factors
In full
A factor both numbers have is a common factor; a multiple both have is a common multiple. You can list them. 12's factors are 1, 2, 3, 4, 6, 12 and 18's are 1, 2, 3, 6, 9, 18: in both lists are 1, 2, 3 and 6, the common factors, and 1 is always one of them. 4's multiples are 4, 8, 12, 16, 20, 24…, and 6's are 6, 12, 18, 24…: 12, 24, 36… are in both, the common multiples, and they never end. Another way: find the highest common factor, 6, and its factors 1, 2, 3, 6 are all the common factors; find the lowest common multiple, 12, and its multiples are all the common multiples.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Which of these is a common factor of 12 and 14?
- A. 6
- B. 13
- C. 2
- D. 7
Choose the right answer
Show the answer and working
Answer: C. 2
12 ÷ 2 = 6 and 14 ÷ 2 = 7, no remainders: 2 is a common factor.
Example 2
The two smallest common multiples of 5 and 6 are □ and □.
Fill in each box
Show the answer and working
Answer: 30，60
List the multiples of 6 and pick those that are also multiples of 5: 30, 60, …
Example 3
How many common factors do 14 and 56 have?
Show the answer and working
Answer: 4
List both sets of factors: the ones in both are the common factors, which are just the factors of 14: 4 of them.
Practise it in the game →Factors and multiples · Free to start, unlimited questions, no download