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#