Step by step
The question
Question: find the greatest common factor of 18 and 24.
GCF(18, 24) = ?
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 18 are 1, 2, 3, 6, 9 and 18.
Factors of 18: = 1, 2, 3, 6, 9, 18
They come in pairs: 1 times 18, 2 times 9, 3 times 6.
1 × 18, 2 × 9, 3 × 6
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Factors of 24: = 1, 2, 3, 4, 6, 8, 12, 24
They come in pairs: 1 times 24, 2 times 12, 3 times 8, 4 times 6.
1 × 24, 2 × 12, 3 × 8, 4 × 6
2 Find the common ones
1, 2, 3 and 6 are in both lists.
These are the common factors.
Common: = 1, 2, 3, 6
3 Pick the greatest
The greatest one is 6.
So the GCF is 6.
GCF(18, 24) = 6
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: 6 goes into each number.
18 ÷ 6 = 3
24 ÷ 6 = 4
No numbers are left over.
So 6 is right!
Let's look back.
First: list the factors.
Then: find the common ones.
Then: pick the greatest.
Last: check.
Answer
GCF(18, 24) = 6