Greatest Common Factor via Ladder Method

Greatest Common Factor

Using the Ladder Method

Mathematics | 6th Grade

What is the Greatest Common Factor?

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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Draw

Find the G.C.F. of 12 and 28 using the listing method.

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​

​2	​12	​28
​2	​6	​14
​	​3	​7

​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

Multiple Choice

What is the correct way to find the G.C.F. of two given numbers using the ladder method?

• 1. Write the given numbers on a line and draw an L around them.

  2. Identify a shared prime and divide the numbers by it.

  3. Write the new numbers on a new line and repeat the process.

  4. After finding all the shared primes, multiply them together.

• 1. Solve for prime factorization.

  2. Multiply the primes of both numbers together.

• 1. List all the factors for the two numbers.

  2. Identify the G.C.F of the listed factors.

Draw

Find the G.C.F. of 30 and 84 using the ladder method.

Multiple Choice

What is the G.C.F. of 20 and 32?

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