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The greatest common factor is 7a.

21ab+35a

=7a(3b+5)
GCF(21ab, 35a) = 7a. How? Factor out each term to get:

21ab = 3 x 7 x a x b

35a = 5 x 7 x a

The factors that occur both in 21ab and 35a are 7 and a. Therefore, the GCF is 7a.

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