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Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 GCSE Maths Starter 9 1) Describe the Correlation in the scatter graph below.. 2. Expand 5(x – 3) 3. Simplify y⁵ x y³ 4. What is 304 ÷ 8 5. What is 60⁰C converted into ⁰F? Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 • 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 What are the first five multiples of: 3, 6, 9, 12, 15 a) 3 4, 8, 12, 16, 20 b) 4 11, 22, 33, 44, 55 c) 11 21, 42, 63, 82, 105 d) 21 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 Identify the prime numbers in the grid below. There are 7 to find. 7 X 45 X 22 X 39 23 63 17 9 57 81 X X X X 77 11 27 X X 19 99 X X 37 X1 69 X 2 49 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 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 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 Find the LCM of the following: a) 2 and 5 10 b) 3 and 4 12 c) 4 and 8 8 d) 5 and 6 30 e) 3 and 8 24 f) 4 and 9 36 g) 8 and 10 40 h) 4, 5 and 12. 60 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 What are the factors of: 1, 2, 4, 8, 16 a) 16 1, 2, 5, 6, 15, 30 b) 30 1, 2, 4, 8 c) 8 1, 7 d) 7 A factor is a whole number which divides exactly into a whole number, leaving no remainder. A prime number has exactly two factors: 1, and the number itself. Factors Are Certainly Tiny Or Really Small Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 • Highest Common Factor (HCF) – the number that goes into two or more numbers exactly. • Write out all the factors for each number…. • Example: Find the HCF of 32 and 56 32 1, 2, 4, 8, 16, 32 56 1, 2, 4, 7, 8, 14, 28, 56 HCF = 8 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 Find the HCF of the following numbers: a) 8 and 12 4 b) 9 and 15 3 c) 10 and 30 10 d) 18 and 33 3 e) 32 and 80 16 f) 60 and 108 12 g) 36, 64, and 76 4 h) 48, 60 and 84 12 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 • 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 • Example: Write 84 as a product of its prime factors 84 2 42 2 • 84 = 2 x 2 x 3 x 7 • 84 = 22 x 3 x 7 21 3 7 • Now your turn: Write 42 as a product of prime factors. Your turn… 1. Find the HCF of the following: a) b) c) d) e) f) 18 and 28 16 and 40 42 and 90 40 and 63 20, 64 and 108 54, 90 and 162 2 8 6 1 4 18 2. Find the LCM of the following: a) b) c) d) e) f) 4 and 5 8 and 12 6 and 9 12 and 15 5, 8 and 10 4, 7 and 9 20 24 18 60 40 252 3. Write the following as products of their prime factors. a) 18 32 x2 b) 135 33 x 5 c) 154 2 x 7 x 11 d) 2310 2 x 3 x 5 x 7 x 11 Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96 • 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)