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Common factor of three terms

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The question

30x² + 18x + 18

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)
  1. First look for a factor every term shares. The numbers here are 30, 18, 18 — find the biggest number that divides all of them.
  2. 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.
  3. 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.
  4. Check the bracket: 5x² + 3x + 3 — those numbers share nothing but 1, so nothing more comes out. 30x² + 18x + 18 = 6(5x² + 3x + 3).

How it works.

  1. 01

    First look for a factor every term shares. The numbers here are 30, 18, 18 — find the biggest number that divides all of them.

  2. 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.

  3. 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.

  4. 04

    Check the bracket: 5x² + 3x + 3 — those numbers share nothing but 1, so nothing more comes out. 30x² + 18x + 18 = 6(5x² + 3x + 3).

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