Finding the Greatest Common Factor

Definition:

factor is a number that divides evenly into a larger number.

For example: 6 is a factor of 24 because 24/6=4. Some other factors of 24 are 2, 3, 4, and 8.

The Greatest Common Factor or GCF of two numbers is the largest number that is a factor in both numbers.

Example: Find the GCF of 12, 24 and 36.

Solution:

Step 1: List the factors of each number.

12 – 1, 2, 3, 4, 6, 12
24 – 1, 2, 3, 4, 6, 8, 12, 24
36 – 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 2: Identify the GCF.
12

OR

Step 1: Write the numbers as a product of their primes.

12: 2*2*3 = 2²*3
24: 2*2*2*3 = 2³*3
36: 2*2*3*3 = 2²*3²

Step 2: Keep the highest power of each prime.

2²*3 = 12

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