How do you find the greatest common factor of #35n^2m, 21m^2n#?

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Answer 1 · 2016-12-01T22:38:22

The GCF is #7mn#.

Find the greatest common factor (GCF) of #35n^2m# and #21m^2n#.

First find the GCF, or the largest number that goes into both, of #35# and #21#.

#35# has factors #1, 5,7,35#.

#21# has factors #1,3,7,21#.

The greatest (or largest) number common to both lists is #7#.

Next find the GCF of the variables.. The largest power of #m# common to both terms is #m#. The largest power of #n# common to both term is #n#.

Thus, the GCF is #7mn#.