How to Find the Highest Common Factor
The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers.
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| Before we begin we first need to be able to : | Practice Questions |
| Know what are the factors of a number | Find the factors of the following numbers. Questions |
| Know what are prime numbers | Identify the prime numbers. Questions |
| Know what are prime factors | Find the Prime factors of the following Questions |
Now that we have learnt how to find the prime factors of a number, we look for the prime factors that are common and multiply them.
EXAMPLE 1
Find the GCF of these pairs of numbers.
14, 49
Solution: List the prime factors of each.
14: 2 × 7
49: 7 × 7
7 is the only common factor; therefore, 7 is the HCF.
EXAMPLE 2
15, 75
Solution: List the prime factors of each.
15: 3 × 5
75: 3 × 5 × 5
3 and 5 are common; therefore, 3 × 5 = 15 is the HCF.