First factor the each term in the expression.
\44x3 = 2 · 2 · 11 · x · x · x
\24x2 = 2 · 2 · 2 · 3 · x · x
\The GCF is the product of the common prime factors in each term.
\GCF = 2 · 2 · x · x = 4x2
The greatest common factor of 44x3and 24x2 is 4x2.