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How to Make a Factor Tree in 5 Easy Steps

Factor trees are useful tools that help chart the numbers by which a larger number is divisible. When you finish a factor tree, you should be able to multiply all the factors and come up with your original number. The length of a factor tree will vary depending on how many factors the original number contains, but this example shows one that can be completed in five steps.

Things You'll Need

  • Paper
  • Pencil
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Instructions

    • 1

      Write the number you want to factor at the top of the paper. In this example, we'll use 210.

    • 2

      Make the second level of the factor tree. Pick any number that divides evenly into the top number. You can choose any number; for example, if you divide 210 by 2, you get 105. So the second level of the factor tree consists of two branches, 2 and 105. Draw two lines branching out from beneath 210 in a teepee shape; write 2 under the line on the left and 105 under the line on the right.

    • 3

      Continue to the next level. The number 2 can't be broken down any further, so leave it alone and concentrate on 105. Since you can divide 105 evenly by 5 --- 5 times 21 equals 105 --- use that number to create the next level. Draw two lines branching out from 105 and write 5 under the left line and 21 under the right line.

    • 4

      Complete the fourth level of the factor tree, dealing with 5 and 21. Leave 5 alone, because it can't be broken down any further, and concentrate on 21. The latter is a product of 3 and 7, so draw two lines branching out from 21 and write 3 under the left line and 7 under the right line. Since neither 3 nor 7 can be broken down further, this is the final level of the factor tree.

    • 5

      Write down all of the numbers that could not be broken down further --- these are the factors of the top number. So, in this example, 2, 5, 3 and 7 are factors of 210.

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