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GCSE Foundation
Numbers Index

GCSE Maths Foundation Level

Numbers - Common Factors

What do we mean by common factors?
Numbers that are factors of two numbers.

Can you show me an example?
Yes, it is much easier to see with an example.

What are the common factors of 4 and 6?

Factor pairs of 4 are
1 × 4
2 × 2
So the factors of 4 are 1, 2 and 4
1    2    4

Factor pairs of 6 are
1 × 6
2 × 3
So the factors of 6 are 1, 2, 3 and 6
1    2    3    6

1    2    4
1    2    3    6
The ones that are factors of both 4 and 6 are 1 and 2

How much should I show to make the method clear
AND for me to be able to check my work?

What are the common factors of 4 and 6?

Factor pairs of 4
1 × 4
2 × 2
Factors of 4
1    2    4

Factor pairs of 6
1 × 6
2 × 3
Factors of 6
1    2    3    6

1    2    4
1    2    3    6

Answer ............ 1 and 2

If I feel a bit more confident
could I show a bit less working but still make the method clear?

What are the common factors of 4 and 6?

[4]
1 × 4
2 × 2
1    2    4

[6]
1 × 6
2 × 3
1    2    3    6

Answer ............ 1 and 2

SAMPLE QUESTION

How many common factors have the numbers 8 and 24?
Question:

So all numbers will have the common factor of 1?
Yes

What are the common factors of 45 and 60?

[45]
1 × 45
3 × 15
5 × 9
1    3    5    9    15    45

[60]
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
1    2    3    4    5    6    10    12    15    20    30    60

Answer ............ 1, 3, 5 and 15

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