The Singing Hedgehog Guide to:

Prime Factors 6 - Finding the HCF

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Prime Factors 6 - Finding the HCF

If
we have two or more numbers, expressed as the product of their prime
factors, we can easily find the Highest Common Factor [the largest
number that divides into all the values].

All we do is multiply together every factor that is common to all the values.

Example: Find the HCF of 24, 42 and 60

24 = 2 x 2 x 2 x 3

42 = 2 x 3 x 7

60 = 2 x 2 x 3 x 5

The factors common to all three are 2 and 3 so the HCF is 6.

Harder Example: Find the HCF of 180, 420, 600.

180 = 2 x 2 x 3 x 3 x 5

420 = 2 x 2 x 3 x 5 x 7

600 = 2 x 2 x 2 x 3 x 5 x 5

The common factors are 2, 2, 3 and 5 so the HCF is 60.

Prime Factors Cancelling fractions All we do is multiply together every factor that is common to all the values.

Example: Find the HCF of 24, 42 and 60

24 = 2 x 2 x 2 x 3

42 = 2 x 3 x 7

60 = 2 x 2 x 3 x 5

The factors common to all three are 2 and 3 so the HCF is 6.

Harder Example: Find the HCF of 180, 420, 600.

180 = 2 x 2 x 3 x 3 x 5

420 = 2 x 2 x 3 x 5 x 7

600 = 2 x 2 x 2 x 3 x 5 x 5

The common factors are 2, 2, 3 and 5 so the HCF is 60.

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