The greatest common factor (GCF) is the greatest algebraic expression that is a factor of two or more expressions. The first step for finding a GCF is to break down each number into its prime factors. We will write down all of the prime factors that are common between the given numbers.
Given Expression
Prime Factorization
Common Prime Factors
100xy
2* 2 * 5 * 5 * x * y
5, 5, x, y
75xyz
3 * 5 * 5 * x * y * z
5, 5, x, y
For the given expressions, the common prime factors are 5, 5, x, and y. The next step is to calculate the product of these factors.
5 * 5 * x * y = 25xy
