What is the greatest common factor of 108 and 168?

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Answer 1 · 2016-04-08T17:32:04

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

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

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

Hence Greatest Common Factor is $12$

Answer 2 · 2016-04-08T18:26:01

$12$

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:

$168/108 = 1$ with remainder $60$

$108/60 = 1$ with remainder $48$

$60/48 = 1$ with remainder $12$

$48/12 = 4$ with remainder $0$

So the GCF is $12$