Highest Common Factor (HCF)
Learn with examples, then test your knowledge!
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides two or more numbers without leaving a remainder.
Examples
Find the HCF of 12, 18 and 24
| 2 | 12 | 18 | 24 |
| 3 | 6 | 9 | 12 |
| 2 | 3 | 4 |
The highest common factor is 2 × 3 = 6
Find the HCF of 24, 36 and 192
| 2 | 24 | 36 | 192 |
| 2 | 12 | 18 | 96 |
| 3 | 6 | 9 | 48 |
| 2 | 3 | 16 |
The highest common factor is 2 × 2 × 3 = 12
Find the HCF of 8, 9 and 25
We check for common prime factors (2, 3, 5...). Since none can divide all three numbers, the process stops immediately.
| 8 | 9 | 25 |
The only number that divides all of them is 1. The HCF is 1, so the numbers are co-prime.
Practice Zone
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