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Prime factor decomposition

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Prime factor decomposition

1. 1. Objective Be able to write a number as the product of prime factors
2. 2. Remember the prime numbers? 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …. Here are the first ten prime numbers: Why are they prime? Each number has only two natural factors. In every case the two factors are the number itself and the number 1 The factors of 2 are 1 and 2 The factors of 3 are 1 and 3
3. 3. Prime factor decomposition Write the number 36 as the product of its prime factors 36 Think of two numbers which multiply together to give 36. We could use 2 and 18 2 18 Now ask yourself, “are these prime numbers?” Is 2 a prime number? Yes. So we can stop this part of our tree here. Is 18 a prime number? No. So we carry on 2 2 9 3 3 2 3 3 36 = 2 x 2 x 3 x 3 36 = 22 x 32
4. 4. Prime factor decomposition Write the number 28 as the product of its prime factors 28 Think of two numbers which multiply together to give 28. We could use 7 and 4 7 4 Now ask yourself, “are these prime numbers?” Is 7 a prime number? Yes. So we can stop this part of our tree here. Is 4 a prime number?No. So we carry on 2 7 2 2 28 = 2 x 2 x 7 28 = 22 x 7 2