Factors of a number are the integers (whole numbers) that divide into it without any remainders or decimals.

Factors can also be thought of as the times tables in which a number appears.

Every number have a finite amount of factors (numbers with exactly two factors are called the prime numbers).

For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Common factors of two numbers are factors that they both have.

For example, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

So, the common factors of 36 and 48 are 1, 2, 3, 4, 6 and 12.

The highest common factor is the largest of all the common factors. In this example, the highest common factor (HCF) is 12.

Now let's try to find the higgest common factor for the numbers 44 and 72.

Factors for 44: 1, 2, 4, 11, 22, 44.

Factors for 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So the highest common factor is 4.

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Edexcel Calculator Paper November 2010 (H) - Page 18, Question 20 

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