What is the greatest common factor of 24 and 42?

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Answer 1 · 2016-04-16T20:28:31

Break the numbers down into their prime number factors.

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

Tony B

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 · 2016-04-19T21:31:55

$6$

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

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 $6$