Factoring and Multiples

What is the greatest common factor of 45 and 69?


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Answer: 3

Definition: A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that the numbers have in common.


One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them.

The factors of 45 are 1, 3, 5, 9, 15, and 45.

The factors of 69 are 1, 3, 23, and 69.

The common factors are 1 and 3. Therefore, the greatest common factor is 3.