Prealgebra for Two-Year Colleges/Appendix (procedures)/Greatest common factor

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The greatest common factor (GCF) can be found in a similar fashion. In this case, the product of the prime factors common to all the numbers gives the HCF.

For example, if we wish to find the HCF of 60, 12 and 102 we write

60=2^2 \cdot 3 \cdot 5 \\
12=2^2 \cdot 3 \\
102=2 \cdot 3 \cdot 17 

Now the GCF is 2 \cdot 3=6.

Two numbers which have an HCF of 1, for example 12 and 5, are said to be coprime - they have no factors in common (except 1).