# Greatest Common Factor

The **Greatest Common Factor (GCF)**, also called the **Highest Common Factor (HCF)**, is the largest number that will divide into two given numbers.

To find the GCF, list all the **prime factors** of each given number from smallest to largest. **Start by dividing by 2, then 3, then 5, then 7, then 11 and so on**.

## Examples

NUMBERS | ALL FACTORS | GREATEST COMMON FACTOR |

18 | 2 × 3 × 3 | 2 and 3 are common of both 18 and 24. The GCF of 18 and 24 is 6, that is, 2 × 3. |

24 | 2 × 2 × 2 × 3 |

NUMBERS | ALL FACTORS | GREATEST COMMON FACTOR |

42 | 2 × 2 × 3 × 7 | 2 and 7 are common factors of both 42 and 70. The GCF of 42 and 70 is 14, that is, 2 × 7. |

70 | 2 × 5 × 7 |

## Questions

Find the Greatest Common Factor of each of these sets of numbers.
**Q1.** 12, 28
**Q2.** 30, 54
**Q3.** 14, 22, 38

**Answer**
**A1.** 4
**A2.** 6
**A3.** 2