Greatest Common Factor

- - Pre-Algebra

The greatest common factor (GCF) of two or more counting numbers is the greatest counting number that divides all the given numbers. If that number is 1, then the two numbers are said to be relatively prime.

To find the GCF of two or more counting numbers, follow the following steps:

1. List the prime factors of each number.
2. Multiply those factors both or among numbers have in common. If there are no common prime factors, it is understood that the greatest common factor (GCF) is 1.
Examples:

1. Find the GCF of 6 and 14.

SOLUTION:

we think of a number, usually prime, that divides both the numbers 6 and 14, then we apply continuous division as shown below.

The GCF of 6 and 14 is 2. This can be written as $GCF(6,14)=2$.

2. Find the GCF of 8, 16 and 40.

SOLUTION:

Therefore, the

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