Greatest Common Factor

Greatest Common Factor (GCF) or Highest Common Factor (HCF) is the largest of the common factors.

Greatest Common Factor is useful to simplify a fraction, because it is the largest number we can divide both numerator and denominator of a fraction.

How to Find the Greatest Common Factor

Method 1

  • find all factors of both numbers,
  • find the ones that are common to both
  • choose the greatest.

Example

Simplify 9/12

NumberFactorsCommon FactorsGreatest Common FactorSimplified Fraction
9 and 12{1,3,9} and {1,2,3,4,6,12}1,33Greatest Common Factor (GCF)

Method 2

  • find the prime factors
  • combine the common ones together

Example

Simplify 24/108

NumberFactorsGreatest Common FactorSimplified Fraction
24 and 108{2 × 2 × 2 × 3} and {2 × 2 × 3 × 3 × 3} 2 × 2 × 3 = 12Greatest Common Factor (GCF) Example

Learn More

Common Factor

Table of Factors and Multiples

Reciprocal of Number

Simplifying Square Roots

Numbers Index

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