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.

Table of Contents

## 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

Number | Factors | Common Factors | Greatest Common Factor | Simplified Fraction |

9 and 12 | {1,3,9} and {1,2,3,4,6,12} | 1,3 | 3 |

### Method 2

- find the prime factors
- combine the common ones together

#### Example

Simplify 24/108

Number | Factors | Greatest Common Factor | Simplified Fraction |

24 and 108 | {2 × 2 × 2 × 3} and {2 × 2 × 3 × 3 × 3} | 2 × 2 × 3 = 12 |