Prime Factorisation Factor Trees Whats It All About

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 This is called a factor tree. All the red digits are prime factors of 56. 2 is a prime number and a factor of 56 so 2 is a prime factor of 56. Is 28 a prime factor? 28 2 14 2 A product is the result of multiplying. 56 = 2 2 2 7 No, so repeat the process for 28. 7 56 is an even number so can be written as 2 something. . .

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

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 5 420 = 2 2 5 3 7 21 3 7

Your Turn Draw a factor tree and use it to write each of the following as the product of its prime factors. 1. 2. 3. 4. 5. 72 80 75 648 108

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

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

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

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

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

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