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Fractions

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Common factors and simplest form

Common factors

The factors of a number are those numbers that divide into it exactly.

Numbers have common factors if the same number divides into both of them.

So 4 is a common factor of both 8 and 12, as it divides into both of them. 2 is a common factor of both 2 and 6, as it divides into both of them.

Simplest form

You know that 4/12 = 2/6 = 1/3

4 and 12 have a common factor (4), so 4/12 can be written as 1/3 (divide the top and the bottom by 4).

2 and 6 have a common factor (2), so 2/6 can be written as 1/3 (divide the top and the bottom by 2).

However, 1 and 3 have no common factors, so 1/3 cannot be simplified. When a fraction cannot be simplified we say that it is its simplest form.

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