Method 1:
\Factor the each monomial.
\15xy = 3 · 5 · x · y
\7x2 = 1 · 7 · x · x
\The GCF is the product of the common prime factors in each monomial.
\GCF = x
\ The greatest common factor of 15xy and 7x2 is x.
The greatest common factor of 15xy and 7x2 is x.