Common factor of three terms, step by step
Three terms, one shared factor: 6x² + 9x + 12 all divide by 3.
The question
30x² + 18x + 18
30x² + 18x + 18
301818
30:12356101530
18:1236918
18:1236918
GCF = 6
6(5x² + 3x + 3)
30x² + 18x + 18=6(5x² + 3x + 3)
- Before anything else, look at whether every term shares a factor. The numbers here are 30, 18, 18 — so the question is what the biggest number that divides ALL of them is.
- List what divides each one and look for the biggest they all share. 30: 1, 2, 3, 5, 6, 10, 15, 30 18: 1, 2, 3, 6, 9, 18 18: 1, 2, 3, 6, 9, 18.
- The biggest number in all of those lists is 6. Take it out in front and divide every term by it: 30 ÷ 6 = 5, 18 ÷ 6 = 3, 18 ÷ 6 = 3.
- Check the bracket before you stop. 5x² + 3x + 3 — those numbers share nothing but 1, so there is no more to take out and 6 really was the greatest. 30x² + 18x + 18 = 6(5x² + 3x + 3).
How it works.
- 01
Before anything else, look at whether every term shares a factor. The numbers here are 30, 18, 18 — so the question is what the biggest number that divides ALL of them is.
- 02
List what divides each one and look for the biggest they all share. 30: 1, 2, 3, 5, 6, 10, 15, 30 18: 1, 2, 3, 6, 9, 18 18: 1, 2, 3, 6, 9, 18.
- 03
The biggest number in all of those lists is 6. Take it out in front and divide every term by it: 30 ÷ 6 = 5, 18 ÷ 6 = 3, 18 ÷ 6 = 3.
- 04
Check the bracket before you stop. 5x² + 3x + 3 — those numbers share nothing but 1, so there is no more to take out and 6 really was the greatest. 30x² + 18x + 18 = 6(5x² + 3x + 3).