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# Factors and multiples

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### Factors and multiples

1. 1. GCSE Maths RevisionFactors and Multiples Adam Mlynarczyk www.mathstutor4you.com 1
2. 2. Factors and MultiplesKey Facts:Factors of a number divide into it exactly.Multiples of a number can be divided by itexactly.Common factors and multiples belong to twodifferent numbers.Every number can be written as the product ofits prime factors. www.mathstutor4you.com 2
3. 3. FactorsThe factors of a whole number are thenumbers that divide into it exactly. The factors of 12 are 1 2 1, 2, 3, 4, 6 and 12. They link up in pairs: 12 12 6 1 x 12 = 12, 3 4 2 x 6 = 12, 3 x 4 = 12 www.mathstutor4you.com 3
4. 4. FactorsThe factors of a whole number are thenumbers that divide into it exactly. 1 25 has only three factors: 1, 5 and 25. 5 links with itself. Numbers like this are called 25 square numbers.25 5 1 x 25 = 25, 5 x 5 = 25, www.mathstutor4you.com 4
5. 5. Factors The factors of a whole number are the numbers that divide into it exactly. 1 Numbers that have only two factors are prime. They can only be divided exactly by 1 or themselves. 17 is an example17 17 of prime number. 1 x 17 = 17,2 is the smallest prime number and is the only evenone. Numbers that are not prime are composite. 5
6. 6. 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
7. 7. Prime factorsEvery whole number can be made bymultiplying prime numbers together. Findinghow to do this is called decomposition.You can use factor tree to decompose anumber. Split every number into two factors.Branches that end in a prime number dontneed 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
8. 8. Prime factors❑❑ 90 2 45 9 5 3 3This tree shows that 90 = 2 x 3 x 3 x 5. Repeatedprime factors can be written using indices: 8 2 90 = 2 x 3 x 5
9. 9. MultiplesIf you multiply a number by 1, 2, 3, 4, … youcalculate its multiples.The multiples of 12 are 12, 24, 36, 48, 60, …Different numbers can share some of the samemultiples. 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 multiplesof 12 and 18. www.mathstutor4you.com 9
10. 10. HCFHCF stand for highest common factor.For example, look at the common factors of 12 and18 listed on slide number 6. The largest is 6, so 6 isthe HCF of 12 and 18.You can use prime factors to find the HCF of twonumbers.Simply pick out the prime factors that are commonto both numbers and multiply them together: 90 = 2 x 3x3x5 If you cant match anything, 120 = 2 x 2 x 2 x 3 x 5 The HCF is 1. 10HCF = 2 x 3 x 5 = 30
11. 11. LCMLCM stands for lowest common multiple. Look atthe common multiples of 12 and 18 listed on theslide number 9. The smallest is 36, so 36 is the LCMof 12 and 18.You can use prime factors to find the LCM of twonumbers.Use the biggest power of each prime factor fromthe two numbers and multiply these together: 90 = 2 x 3x3x5120 = 2 x 2 x 2 x 3 x 5 11LCM = 2 x 2 x 2 x 3 x 3 x 5 = 360
12. 12. Factors and MultiplesPractice questions1. List the factors of these numbers.a) 36b) 27c) 50d) 30 12
13. 13. Factors and MultiplesPractice questions2. Use the list you made in question 1 to write outthe common factors of these pairs of numbers.a) 30 and 36b) 27 and 30c) 50 and 30 13d) 50 and 27
14. 14. Factors and MultiplesPractice questions3. List the first ten multiples of these numbers.a) 6b) 10c) 25d) 35 14
15. 15. Factors and MultiplesPractice questions4. Use the lists you made in question 3 to find somecommon multiples of these pairs of numbers.a) 6 and 10b) 25 and 35c) 10 and 35 15d) 6 and 25
16. 16. Factors and MultiplesPractice questions5. Write these numbers as the product of their primefactors.a) 36b) 42c) 40 16d) 63
17. 17. Factors and MultiplesPractice questions6. Use the answers from question 5 to find the HCFand LCM of these pairs of numbers.a) 36 and 42b) 36 and 40c) 42 and 63 17d) 40 and 63
18. 18. Factors and MultiplesNotes: www.mathstutor4you.com 18
19. 19. Factors and MultiplesNotes: www.mathstutor4you.com 19
20. 20. Factors and MultiplesNotes: www.mathstutor4you.com 20
21. 21. Factors and MultiplesNotes: www.mathstutor4you.com 21
22. 22. Thank you Thank you for joining my online class! It was my pleasure to teach you! I hope to see you again soon!In order to be notified about my new GCSE Revision classes, please follow me on the WiZiQ website at: www.wiziq.com/adammlynarczykPlease do not forget to leave feedback about my free online class! www.mathstutor4you.com 22

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