What is the GCF of 16, 24, and 32?

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3
Apr 5, 2016

$8$

Explanation:

Working out all the factors of 16, 24 and 32, you will find that 8 is the greatest one that all of them share.

Also, you cannot have a factor that is greater than half of the lowest number, so 8 is the greatest possible factor of 16. It is also the difference between all the numbers, so it is a good place to begin.

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2
Feb 14, 2017

$G C F = 2 \times 2 \times 2 = 8$

Explanation:

Write each number as the product of its prime factors.

It is then very easy to see exactly what factors they have in common.

$16 = \textcolor{red}{2 \times 2 \times 2} \times 2 \text{ } = {2}^{4}$
$32 = \textcolor{red}{2 \times 2 \times 2} \times 2 \times 2 \text{ } = \textcolor{b l u e}{{2}^{5}}$
$24 = \textcolor{red}{2 \times 2 \times 2} \times \textcolor{w h i t e}{\times \times x} 3 \text{ } = {2}^{3} \times \textcolor{b l u e}{3}$

$G C F = \textcolor{red}{2 \times 2 \times 2} = 8 \text{ } \leftarrow$ multiply together

From this, the LCM can also be found easily.

$L C M = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = \textcolor{b l u e}{{2}^{5} \times 3} = 96$

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .}$ Use a factor from each column

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