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GREATEST COMMON FACTOR

Definition of Greatest Common Factor

Greatest common factor is the greatest number that is a factor of each of two or more given numbers.

More About Greatest Common Factor

Greatest Common Factor is abbreviated as G.C.F
Greatest common factor of two or more numbers can be found by successive division method and factorization method

Examples of Greatest Common Factor:

The greatest common factor of 24 and 15 is 3
The greatest common factor of 40, 50, and 25 is 5


Video Examples: Greatest Common Factor - GCF


Solved Examples on Greatest Common Factor

Ques: Which is the greatest common factor of 20 and 36?

Choices:
  • A. 20
  • B. 4
  • C. 36
  • D. 180

Correct Answer: B

Solution:

  • Step 1: The factors of 20 are 1, 2, 4, 5, 10, 20
  • Step 2: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
  • Step 3: The common factors of 20 and 36 are: 1, 2, 4
  • Step 4: So, the greatest common factor or G.C.F. of 20 and 36 is 4

Ques: What is the G.C.F. of 45 and 75?

Choices:
  • A. 5
  • B. 10
  • C. 15
  • D. 20

Correct Answer: C

Solution:

  • Step 1: Divide the larger number 75 by 45. The remainder will be 30

    Examples of Greatest Common Factor

  • Step 2: Divide 45 with the remainder 30. This time, the remainder is 15.

    Greatest Common Factor Examples

  • Step 3: Finally, divide 30 with the remainder 15. The remainder is 0.

    Examples of GFC

  • Step 4: Therefore, the G.C.F. of 45 and 75 is 15

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