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Prime Factorisation Factor Trees

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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.

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Example 1 Write 56 as a product of its prime factors.

56 is an even number so can be written as 2 something… List the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19… 56 28 28 is not a prime number, so repeat the process 2 This is called a factor tree. All the red digits are prime factors of 56. 2 14 14 is not a prime number, so repeat the process 2 7 A product is the result of multiplying. 7 is a prime number, so stop the process 56 = 2 2 2 7

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Example 2 Write 81 as a product of its prime factors.

81 is an odd number and is divisible by prime number 3 List the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19… 81 27 27 is not a prime number, so repeat the process 3 This is called a factor tree. All the red digits are prime factors of 81. 3 9 9 is not a prime number, so repeat the process 3 3 A product is the result of multiplying. 3 is a prime number, so stop the process 81 = 3 3 3 3 This is not the only possible factor tree, but any factor tree should give the same end result!

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Example 3 Write 420 as a product of its prime factors. 420 is an even number so can be written as 2 something… 420 List the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19… 210 is not a prime number, so repeat the process 210 2 105 is not a prime number, so repeat the process This is called a factor tree. All the red digits are prime factors of 420. 2 105 35 is not a prime number, so repeat the process 3 35 7 is a prime number, so stop the process 5 7 A product is the result of multiplying. 420 = 2 2 3 5 x 7 This is not the only possible factor tree, but any factor tree should give the same end result!

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

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