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Factor trees and the product of prime factors. Easy method with examples.

Updated on March 14, 2013

Product Of Prime Factors Video

A factor tree can be used to express a number as a product of prime factors. Make sure you know your first 5 prime numbers before you start these examples. These are 2,3,5,7 and 11 (a prime number can only be divided by 1 and itself).

Example 1

Write down 140 as a product of prime factors.

First think of two numbers that multiply together to give 140.

Let’s go with 2 × 70.

2 is a prime number (so circle it) and 70 is not a prime number, so 70 needs to be split into another pair of factors.

Let’s write 70 as 7 × 10.

Now, 7 is a prime number and 10 is not prime. Circle the 7, and split the 10 into another factor pair.

10 can be written as 2 × 5. 2 and 5 are both prime numbers so circle the 2 and 5.

Now all the numbers that we have circled are prime factors of 140 and if you multiply these prime factors together it will give you 140. So the product of prime factors is:

2 × 2 × 5 × 7.

This can also be written using powers as 2 × 2 × 5 × 7.

Example 2

Write down 252 as a product of prime factors.

First think of two numbers that multiply together to give 252.

Let’s go with 2 × 126.

2 is a prime number (so circle it) and 126 is not a prime number, so 126 needs to be split into another pair of factors.

Let’s write 126 as 2 × 63.

Now, 2 is a prime number and 63 is not prime. Circle the 2, and split the 63 into another factor pair.

63 can be written as 7 × 9. 7 is a prime number (so circle it) and 9 is not a prime number, so 9 needs to be split into another pair of factors.

9 can be written as 3 × 3. 3 is prime so circle both 3’s.

Now all the numbers that we have circled are prime factors of 252 and if you multiply these prime factors together it will give you 252. So the product of prime factors is:

2 × 2 × 3 × 3 × 7 or 2² × 3² × 7

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