Greatest Common Factor via Ladder Method

The Greatest Common​ Factor (G.C.F.) of a set of numbers is the largest factor that all the numbers share.

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​A factor is a number or quantity that when multiplied with another produces a given number or expression​.

Greatest Common Factor

The listing method of finding the G.C.F. is shown to the right.

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By listing all the factors of the given numbers, the G.C.F. can be easily identified.​

​Greatest Common Factor

​Listing Method

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By using Prime Factorization, the G.C.F. can be identified by using the shared prime numbers of any two given numbers.

​Greatest Common Factor

​Ladder Method

1. Write the two numbers on a line and draw an L shaped line around them.

2. ​Determine a shared factor.

   1. Hint: Start from 2 and work up.

3. Write the shared factor to the left of the row​ and divide the numbers.

4. Write the new numbers below the previous ones and repeat the process​.

Greatest Common Factor​

​After you can no longer divide the numbers by the same number, multiply the numbers on the left to find the G.C.F. of the original numbers.

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​Therefore, the G.C.F. of 12 and 28 is 4.

2 x 2 = 4