
Find the GCF of 10x3y4z, 15x5y and 25x2y7z3.

The greatest common factor of the expressions
Answer to Problem 1PCT
The greatest common factor of the expressions
Explanation of Solution
Procedure used:
Greatest common factor:
“Step 1: Find the GCF of the coefficients of each variable expression.
Step 2: For each variable factor common to all the expressions, determine the smallest exponent to which the variable factor is raised.
Step 3: Find the product of the common prime factors found in Steps 1 and 2. This expression is the GCF”.
Calculation:
In order to find the GCF of the expressions
The coefficients in the expressions,
The common factor in the numbers 10, 15 and 25 is 5.
Thus, the GCF of the numbers 10, 15 and 25 is 5.
Now, determine the smallest exponent that is common in the monomials
Write the monomials
Note that, the monomials
Since the variable y is common to
Note that, z is common in the first and last term but the second term does not contain z.
That is, the GCF does not contain z.
By step 3 of above procedure, the GCF is
Thus, the GCF of the expressions
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