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 |  |