Step by step
The question
Question: find the greatest common factor of 9 and 16.
GCF(9, 16) = ?
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 9 are 1, 3 and 9.
Factors of 9: = 1, 3, 9
They come in pairs: 1 times 9, 3 times 3.
1 × 9, 3 × 3
The factors of 16 are 1, 2, 4, 8 and 16.
Factors of 16: = 1, 2, 4, 8, 16
They come in pairs: 1 times 16, 2 times 8, 4 times 4.
1 × 16, 2 × 8, 4 × 4
2 Find the common ones
1 is in both lists.
It is the only common factor.
Common: = 1
3 Pick the greatest
The greatest one is 1.
So the GCF is 1.
GCF(9, 16) = 1
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: 1 goes into each number.
9 ÷ 1 = 9
16 ÷ 1 = 16
No numbers are left over.
So 1 is right!
Let's look back.
First: list the factors.
Then: find the common ones.
Then: pick the greatest.
Last: check.
Answer
GCF(9, 16) = 1