# What is the greatest common factor of 108 and 168?

Apr 8, 2016

Greatest Common Factor is $12$

#### Explanation:

Factors of $108$ are $\left\{1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 108\right\}$

Factors of $168$ are $\left\{1 , 2 , 3 , 4 , 6 , 7 , 8 , 12 , 14 , 21 , 24 , 28 , 42 , 56 , 84 , 168\right\}$

Common Factors are $\left\{1 , 2 , 3 , 4 , 6 , 12\right\}$

Hence Greatest Common Factor is $12$

Apr 8, 2016

$12$

#### Explanation:

An alternative approach that does not require factoring both numbers first 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:

$\frac{168}{108} = 1$ with remainder $60$

$\frac{108}{60} = 1$ with remainder $48$

$\frac{60}{48} = 1$ with remainder $12$

$\frac{48}{12} = 4$ with remainder $0$

So the GCF is $12$