EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 6 and 10.
6 = 2 * 3 You can divide 6 by 2 or by 3
6 = 1 * 6 You can divide 6 by 1 or by 6
Therefore 1, 2, 3, and 6 are all factors of six.
10 = 2 * 5 You can divide 10 by 2 or by 5
10 = 1 * 10 You can divide 10 by 1 or by 10
Therefore 1, 2, 5, and 10 are all factors of ten.
Both 6 and 10 can be divided by 1 and by 2; 2 is greater than 1, so 2 is the Greatest Common
Factor (G.C.F.) of 6 and 10.
You can also use the prime factorization method to find the Greatest Common Factor:
EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 36 and 54.
36 = 2 * 2 * 3 * 3
54 = 2 * 3 * 3 * 3
Both have 2 * 3 * 3 in common:
Usually you can find the Greatest Common Factor fairly easily by experimenting with possible
divisors:
Start with the smaller number; it is the largest divisor of itself.
Is it a divisor of the
larger number? If so, you have the G.C.F.; if not:
What is the nextlargest divisor of the smaller
number; is IT a divisor of the other number?
Continue until you find a number that will divide
into BOTH. Sometimes only the number '1' will work as a common divisor; for example: 21 and 16 have no common
factor other than 1.
