GCSE Maths Revision Factors and Multiples Adam Mlynarczyk www.mathstutor4you.com 1
Factors and Multiples Key Facts: Factors of a number divide into it exactly. Multiples of a number can be divided by it exactly. Common factors and multiples 'belong' to two different numbers. Every number can be written as the product of its prime factors. www.mathstutor4you.com 2
Factors The factors of a whole number are the numbers that divide into it exactly. 12 1 12 3 4 2 6 The factors of 12 are 1, 2, 3, 4, 6 and 12. They link up in pairs: 1 x 12 = 12, 2 x 6 = 12, 3 x 4 = 12 www.mathstutor4you.com 3
Factors The factors of a whole number are the numbers that divide into it exactly. 1 25 25 has only three factors: 1, 5 and 25. 5 links with itself. Numbers like this are called square numbers. 25 5 1 x 25 = 25, 5 x 5 = 25, www.mathstutor4you.com 4
Factors The factors of a whole number are the numbers that divide into it exactly. 17 1 17 Numbers that have only two factors are prime. They can only be divided exactly by 1 or themselves. 17 is an example of prime number. 1 x 17 = 17, 2 is the smallest prime number and is the only even 5 one. Numbers that are not prime are composite.
Common factors Different numbers can share some of the same factors. These are called their common factors. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 1, 2, 3 and 6 are the common factors of 12 and 18. 6
Prime factors Every whole number can be made by multiplying prime numbers together. Finding how to do this is called decomposition. You can use factor tree to decompose a number. Split every number into two factors. Branches that end in a prime number don't need to be split any further. On the next slide we are going to show that 90 = 2 x 3 x 3 x 5 www.mathstutor4you.com 7
Prime factors 90 2 45 9 5 3 This tree shows that 90 = 2 x 3 x 3 x 5. Repeated prime factors can be written using indices: 90 = 2 x 3 2 x 5 3 8
Multiples If you multiply a number by 1, 2, 3, 4, you calculate its multiples. The multiples of 12 are 12, 24, 36, 48, 60, Different numbers can share some of the same multiples. These are called their common multiples. Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, Multiples of 18: 18, 36, 54, 72, 90, 108, 36, 72 and 108 are the first three common multiples of 12 and 18. www.mathstutor4you.com 9
HCF HCF stand for highest common factor. For example, look at the common factors of 12 and 18 listed on slide number 6. The largest is 6, so 6 is the HCF of 12 and 18. You can use prime factors to find the HCF of two numbers. Simply pick out the prime factors that are common to both numbers and multiply them together: 90 = 2 x 3 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 HCF = 2 x 3 x 5 = 30 If you can't match anything, The HCF is 1. 10
LCM LCM stands for lowest common multiple. Look at the common multiples of 12 and 18 listed on the slide number 9. The smallest is 36, so 36 is the LCM of 12 and 18. You can use prime factors to find the LCM of two numbers. Use the biggest power of each prime factor from the two numbers and multiply these together: 90 = 2 x 3 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 LCM = 2 x 2 x 2 x 3 x 3 x 5 = 360 11
Factors and Multiples Practice questions 1. List the factors of these numbers. a) 36 b) 27 c) 50 d) 30 12
Factors and Multiples Practice questions 2. Use the list you made in question 1 to write out the common factors of these pairs of numbers. a) 30 and 36 b) 27 and 30 c) 50 and 30 d) 50 and 27 13
Factors and Multiples Practice questions 3. List the first ten multiples of these numbers. a) 6 b) 10 c) 25 d) 35 14
Factors and Multiples Practice questions 4. Use the lists you made in question 3 to find some common multiples of these pairs of numbers. a) 6 and 10 b) 25 and 35 c) 10 and 35 d) 6 and 25 15
Factors and Multiples Practice questions 5. Write these numbers as the product of their prime factors. a) 36 b) 42 c) 40 d) 63 16
Factors and Multiples Practice questions 6. Use the answers from question 5 to find the HCF and LCM of these pairs of numbers. a) 36 and 42 b) 36 and 40 c) 42 and 63 d) 40 and 63 17
Factors and Multiples Notes: www.mathstutor4you.com 18
Factors and Multiples Notes: www.mathstutor4you.com 19
Factors and Multiples Notes: www.mathstutor4you.com 20
Factors and Multiples Notes: www.mathstutor4you.com 21
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