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# What is a factor tree?

**A factor tree is a diagram that shows the breakdown of a number into its prime factors.** This diagram holds a pattern similar to a family tree, with a line between each factor and its factors.

A factor tree breaks a number into its prime numbers. Prime numbers are numbers above one that cannot be divided by any number besides one and itself while remaining a whole number.

The factor tree for 32 begins with 32 at the top. A line points down to 4 x 8 below the 32. A line then points down from the 4 to 2 x 2. A line points down from the 8 to 2 x 4 and below that, from the 4 to 2 x 2. Each of these sets of numbers breaks down to 2 x 2 x 2 x 2 x 2. Therefore, 32 can be factored to 2 x 2 x 2 x 2 x 2.

Seventy-five can be factored to 3 x 5 x 5. The number 220 can be factored to 2 x 2 x 5 x 11, and the number 1,084 can be factored to 2 x 2 x 271. The number 2,160 can be factored to 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5.

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