Finding the Greatest Common Factor
For Example: For the numbers 18 and 27, 3 is a common factor, but 9 is
common factor , since 9 is the largest number that divides into 18 and 27
Finding the GCF: One approach to finding the GCF is looking at the
prime factors that
occurs the least (look for the smallest exponent ) in each of the numbers or expressions
that are involved. For instance, in the previous example , 18 and 27, factor each number
into its prime factors.
Another example of finding the GCF of 90 and 120:
The least exponent of each factor is one so the GCF is 2●3●5 = 30.
Example: Find the GCF of 12x2y3w and 20xy2.
Example: Find the GCF of 3x3 + 6x2 and 6x2 – 24
The GCF is 3(x + 2)