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Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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GCSE Maths Starter 9 2.Expand 5(x – 3) 3.Simplify y⁵ x y³ 4.What is 304 ÷ 8 5.What is 60⁰C converted into ⁰F? 1) Describe the Correlation in the scatter graph below..

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To identify factors, multiples, squares and prime numbers To find the prime factor decomposition of positive integers To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers EXTN: To solve real life problems involving HCF and LCM.(Grade C) Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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What are the first five multiples of: a)3 b)4 c)11 d)21 3, 6, 9, 12, 15 4, 8, 12, 16, 20 11, 22, 33, 44, 55 21, 42, 63, 82, 105 A multiple of a number is what you get when you multiply that number by some other whole number. Multiples are Usually Larger Than Individual numbers, Possibly Larger never Ever Smaller Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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7 11 19 23 2 17 3749 9 2245 63 5781 27 69 77 99 1 X 7 23 17 11 19 X X 2 XX X X X XXX X X 37 39 Identify the prime numbers in the grid below. There are 7 to find. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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Lowest Common Multiple – the lowest number in two or more numbers’ times tables. Q. Find the LCM of 4 and 6. 1.Write out the first six numbers the 4 and 6 times tables 2.Look for the first number that appears in both lists. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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Example LCM Q.Find the LCM of 4 and 6 4 4, 8, 12, 16, 20, 24,…. 6 6, 12, 18, 24, 30, 36,… We want the LOWEST common multiple, so the LCM of 4 and 6 is… 12 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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a)2 and 5 b)3 and 4 c)4 and 8 d)5 and 6 e)3 and 8 f)4 and 9 g)8 and 10 h)4, 5 and 12. 10 12 8 30 24 36 40 60 Find the LCM of the following: Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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What are the factors of: a)16 b)30 c)8 d)7 1, 2, 4, 8, 16 1, 2, 5, 6, 15, 30 1, 2, 4, 8 1, 7 A factor is a whole number which divides exactly into a whole number, leaving no remainder. Factors Are Certainly Tiny Or Really Small A prime number has exactly two factors: 1, and the number itself. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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HCF = 8 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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a)8 and 12 b)9 and 15 c)10 and 30 d)18 and 33 e)32 and 80 f)60 and 108 g)36, 64, and 76 h)48, 60 and 84 Find the HCF of the following numbers: 4 3 10 3 16 12 4 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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We can use a ‘factor tree’ to enable us to write a number as “a product of its prime factors” Each time you reach a prime number, you stop and circle that number. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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Example: Write 84 as a product of its prime factors 84 = 2 x 2 x 3 x 7 84 = 2 2 x 3 x 7 Now your turn: Write 42 as a product of prime factors. 84 242 221 37 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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Your turn… 1.Find the HCF of the following: a)18 and 28 b)16 and 40 c)42 and 90 d)40 and 63 e)20, 64 and 108 f)54, 90 and 162 2.Find the LCM of the following: a)4 and 5 b)8 and 12 c)6 and 9 d)12 and 15 e)5, 8 and 10 f)4, 7 and 9 3.Write the following as products of their prime factors. a) 18b) 135c) 154d) 2310 2 8 6 1 4 18 20 24 18 60 40 252 3 2 x 2 3 3 x 5 2 x 7 x 11 2 x 3 x 5 x 7 x 11

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To identify factors, multiples, squares and prime numbers To find the prime factor decomposition of positive integers To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers EXTN: To solve real life problems involving HCF and LCM.(Grade C) Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

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