Step by step
The question
Question: find the greatest common factor of 8 and 12.
GCF(8, 12) = ?
A common factor goes into both numbers.
The greatest common factor, the GCF, is the biggest one.
common factor: goes into both
GCF: the greatest one
1 List the factors
The factors of 8 are 1, 2, 4 and 8.
Factors of 8: = 1, 2, 4, 8
They come in pairs: 1 times 8, 2 times 4.
1 × 8, 2 × 4
The factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 12: = 1, 2, 3, 4, 6, 12
They come in pairs: 1 times 12, 2 times 6, 3 times 4.
1 × 12, 2 × 6, 3 × 4
2 Find the common ones
1, 2 and 4 are in both lists.
These are the common factors.
Common: = 1, 2, 4
3 Pick the greatest
The greatest one is 4.
So the GCF is 4.
GCF(8, 12) = 4
Careful: the GCF goes into every number.
So it is never bigger than the smallest one.
Careful: GCF ≤ the smallest number
4 Check
Let's check: 4 goes into each number.
8 ÷ 4 = 2
12 ÷ 4 = 3
No numbers are left over.
So 4 is right!
Let's look back.
First: list the factors.
Then: find the common ones.
Then: pick the greatest.
Last: check.
Answer
GCF(8, 12) = 4