Question

How do you express `36/54` in simplest form?

Answer 1

`36/54 = 2/3`

Explanation:

Note that:

`36 = 2 * 18`

`54 = 3 * 18`

So:

`36/54 = (2 * color(red)(cancel(color(black)(18))))/(3 * color(red)(cancel(color(black)(18)))) = 2/3`

How might we find that greatest common factor (GCF) `18` of `36` and `54` ?

One way of finding the GCF of two numbers goes as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is `0` then the GCF is the smaller number.

• Otherwise repeat with the smaller number and the remainder.

So in our example:

`54 / 36 = 1" "` with remainder `18`

`36 / 18 = 2" "` with remainder `0`

So the GCF of `36` and `54` is `18`.