Prime Factorisation Factor Trees

What’s It All About? You are going to learn: How to write a number as the product of its prime factors. What skills should you have already? You need to know what it means for a number to be a prime number or a factor. You need sound multiplication skills.

Example 1 Write 56 as a product of its prime factors. List the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19... 56 2 is a prime number and a factor of 56 so 2 is a prime factor of 56. Is 28 a prime factor? 2 28 This is called a factor tree. All the red digits are prime factors of 56. 2 No, so repeat the process for 28. 14 2 7 56 is an even number so can be written as 2  something... A product is the result of multiplying. 56 = 2  2  2  7

Example 2 Write 90 as a product of its prime factors. Draw a factor tree: 90 List the first few prime numbers: Is 45 a prime factor? 2 45 No, so repeat the process for 45. 2, 3, 5, 7, 11, 13, 17, 19... 5 9 90 is an even number. 45 is not an even number. 3 This is not the only possible factor tree, but any factor tree should give the same end result! 3 45 is in the 5 times table. 90 = 2  3  3  5

Example 3 Write 420 as a product of its prime factors. Draw a factor tree: 420 2, 3, 5, 7, 11, 13, 17, 19... 2 210 2 105 5 21 3 7 420 = 2  2  5  3  7

Your Turn Draw a factor tree and use it to write each of the following as the product of its prime factors. 72 80 75 648 108

Answers 1. 72 72 2 36 2 18 2 2, 3, 5, 7, 11, 13, 17, 19... 9 3 3 72 = 2  2  2  3  3

Answers 2. 80 80 2 40 2 20 2 10 2, 3, 5, 7, 11, 13, 17, 19... 2 5 80 = 2  2  2  2  5

Answers 3. 75 75 3 25 5 5 2, 3, 5, 7, 11, 13, 17, 19... 75 = 3  5  5

Answers 4. 648 648 2 324 2 126 2 81 2, 3, 5, 7, 11, 13, 17, 19... 9 9 3 3 3 3 648 = 2  2  2  3  3  3  3

Answers 5. 108 108 2 54 2 27 3 9 2, 3, 5, 7, 11, 13, 17, 19... 3 3 108 = 2  2  3  3  3

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