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Common factor of two terms, step by step

Does every term share a factor?

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The question

42x + 6

42x + 6
426
42:12367142142
6:1236
GCF = 6
6(7x + 1)
42x + 6=6(7x + 1)
  1. Before anything else, look at whether every term shares a factor. The numbers here are 42, 6 — so the question is what the biggest number that divides ALL of them is.
  2. List what divides each one and look for the biggest they all share. 42: 1, 2, 3, 6, 7, 14, 21, 42 6: 1, 2, 3, 6.
  3. The biggest number in all of those lists is 6. Take it out in front and divide every term by it: 42 ÷ 6 = 7, 6 ÷ 6 = 1.
  4. Check the bracket before you stop. 7x + 1 — those numbers share nothing but 1, so there is no more to take out and 6 really was the greatest. 42x + 6 = 6(7x + 1).

How it works.

  1. 01

    Before anything else, look at whether every term shares a factor. The numbers here are 42, 6 — so the question is what the biggest number that divides ALL of them is.

  2. 02

    List what divides each one and look for the biggest they all share. 42: 1, 2, 3, 6, 7, 14, 21, 42 6: 1, 2, 3, 6.

  3. 03

    The biggest number in all of those lists is 6. Take it out in front and divide every term by it: 42 ÷ 6 = 7, 6 ÷ 6 = 1.

  4. 04

    Check the bracket before you stop. 7x + 1 — those numbers share nothing but 1, so there is no more to take out and 6 really was the greatest. 42x + 6 = 6(7x + 1).

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