Question

What is the greatest common factor of 24 and 42?

Answer 1

Greatest common factor is 6

Explanation:

Break the numbers down into their prime number factors.

Some prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 ....

Observe that the only prime numbers in both are 2 and 3.

So the product `2xx3=6` is a factor of both.

Since there is no other prime common to both `24` and `42`, we cannot increase the common factor of `6` by multiplying by another prime.

So, the highest/greatest common factor of `24` and `42` is `6`.

Answer 2

`6`

Explanation:

My favourite method for finding the greatest common factor (GCF) of two numbers goes as follows:

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

• If the remainder is zero then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

In our example we find:

`42/24 = 1` with remainder `18`

`24/18 = 1` with remainder `6`

`18/6 = 3` with remainder `0`

So the GCF is `6`