How to Use a Math Factoring Ladder

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Factoring is a method used in mathematics to find the greatest common factor (GCF) for a set of numbers. Many students have experience using a factor tree, but there is another method available that may speed up the process in reaching the numbers' GCF. This method is called the ladder method. Students can also use the ladder method to quickly locate the least common multiple (LCM) for a set of numbers.

Things You'll Need

  • Notebook
  • Pencil

Greatest Common Factor

  • Draw a sideways L on your paper. It will look like an upside down division line.

  • Place the two numbers you are comparing inside the L. Leave a space in between the numbers. Thus, if you are comparing the numbers 6 and 12, you would write the number 6, leave a space and then write the number 12.

  • Choose a prime number that can divide both numbers. For example, 6 and 12 are both divisible by 3. Place the 3 to the left, just outside of the L.

  • Divide the pair of numbers by the prime number and write the answers underneath the L. Underneath the 6, for example, you would have a 2 and underneath the 12, you would have 4. The 2 and the 4 can still be reduced, so draw another L to surround them. Place another prime number on the outside of the L and divide again. For this example, you would use the prime number 2. Underneath the L, you would now have a 1 and a 2. You can stop now since you have only prime numbers left.

  • Multiply all of the prime numbers on the left side of the Ls to find the GCF. In the example, you would need to multiply 3 and 2. The GCF for the pair of 6 and 12 is 6.

Least Common Multiple

  • Draw the L in your notebook like you did when you were working on the GCF. Place the set of numbers you are seeking to find the LCM for inside the L. Again, you need to leave a space in between the two numbers.

  • Select a prime number that divides both numbers. For example, 12 and 30 are both divisible by 3. Put your 3 to the left of the L.

  • Divide the set of numbers by the prime number you entered to the left of the L. The answer should be placed under the L. In the example, a 4 would go under the 12, and a 10 would go under the 30. 4 and 10 are not prime numbers, so another L is needed. Repeat the steps until you only have prime numbers remaining. This example would have another 2 to the left of the L with a 2 and a 5 under the L.

  • Multiply all the numbers to the left of the L and all of the prime numbers underneath of the last L together. The answer is your LCM. The LCM for the numbers 12 and 30 is 60 (3 2 2 * 5).

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