The greatest common factor (GCF) of two (or more) monomials is the product of the greatest common factor of the numerical coefficients (the numbers out in front) and the highest power of every variable that is a factor of each monomial.

Consider: 10x^{2}y^{3} and 15xy^{2}
The greatest common factor is 5xy^{2} .
The largest factor of 10 and 15 is 5.
The highest power of x that is contained in both terms is x.
The highest power of y that is contained in both terms is y^{2}. 

When factoring polynomials, first look for the largest monomial which is a factor of each term of the polynomial. Factor out (divide each term by) this largest monomial.
Factor: 4x + 8y
The largest integer that will divide evenly into 4 and 8 is 4. Since the terms do not contain a variable (x or y) in common, we cannot factor any variables. The greatest common factor is 4. Divide each term by 4.
Answer: 4(x + 2y) 


Factor: 15x^{2}y^{3} + 10xy^{2}
The largest integer that divides evenly into 15 and 10 is 5. The largest power of x present in both terms is x.
The largest power of y present in both term is y^{2}.
The GCF is 5xy^{2}. Divide each term by the GCF.
Answer: 5xy^{2}(3xy + 2) 


