Step by step
The question
Question: write 12 + 18 as a product, using the biggest common factor.
12 + 18
1 Find the GCF
A factor of 12 is a whole number that goes into 12 exactly.
Nothing is left over.
The factors of 12: 1, 2, 3, 4, 6, 12.
The factors of 18: 1, 2, 3, 6, 9, 18.
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
The biggest number in both lists is 6.
= GCF = 6
2 Take it out
12 is 6 times 2.
18 is 6 times 3.
= 6 × 2 + 6 × 3
Both parts have times 6.
So we take the 6 out, in front of a bracket: 6(2 + 3).
This is the distributive property, backwards.
= 6(2 + 3)
Careful!
We need the brackets.
Without them, the 6 times only the 2.
Careful: not 6 × 2 + 3 ✗
3 Check
Let's check: 6 times 5 is 30.
And 12 plus 18 is 30.
The same.
So the answer is right!
6 × 5 = 30 and 12 + 18 = 30
Let's look back.
First: find the GCF.
Then: take it out.
Last: check.
Answer
Careful: not 6 × 2 + 3 ✗