The Highest Common Factor

The highest common factor (HCF) of two or more numbers is the largest number that is a common factor of the numbers. To find it, write down the numbers as their prime factors. Then choose those factors that appear in all of the numbers.

Let’s look at some examples.

Examples

Example 1:

Find the HCF of the numbers 15, 24 and 30.

15=3\times 5

24=2\times 2\times 2\times 3

30=2\times 3\times 5

We see that 3 is common in them all. So the HCF is 3.

Example 2:

Find the HCF of the numbers 16, 24, 72 and 80.

16=2\times 2\times 2\times 2

24=2\times 2\times 2\times 3

72=2\times 2\times 2\times 3\times 3

80=2\times 2\times 2\times 5

We see that 2\times 2\times 2 appears in them all, so the HCF is 8.

Example 3:

Find the HCF of 1245 and 3000.

To find the prime factors, we use the method of long division.

3|1245

5|415

83|83

1

And

2|3000

2|1500

2|750

3|375

5|125

5|125

5|25

5|5

1

So, we have 1245=3\times 5\times 83 and 3000=2\times 2\times 2\times 3\times 5\times 5\times 5

3\times 5 is common in both, therefore HCF is 3\times 5=15

Example 4

Find the HCF of 210, 315, and 650.

We first find the prime factors of each number:

210 = 2 \times 3 \times 5 \times 7

315 = 3^2 \times 5 \times 7

650 = 2 \times 5^2 \times 13

The HCF of 210, 315, and 650 is 5.