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- 1. http://www.education707.com 1 CHAPTER FACTORS AND MULTIPLES Aim The aim of this lesson is to solve problems involving factors and multiples. objective At the end of this lesson, students will be able to understand and solve problems involving Factors Prime factors Highest common factor H.C.F Multiples Least common multiple L.C.M
- 2. http://www.education707.com 2 Factors and multiples Factors Defn. Whole numbers which multiply to give a certain number are called the factors of that number. Ex 1. Factors of 24 are 1 , 24 2 , 12 , 3 , 8 , 4 , 6 , Ex 2. Factors of 36 are 1 , 36 2 , 18 , 3 , 12 , 4 , 9 , 6 , Ex 3. Evaluation Find the factors of 8 , 12 , 9 , 20 and 84
- 3. http://www.education707.com 3 Factors and multiples Prime numbers Defn. Prime numbers are numbers which have exactly two factors, namely 1 and the number itself. Note : 1 is not a prime number because it has only one factor, i.e 1 itself. e.g 2 , 3, 5, 7 , 11 , 13 , 17 , 19 , ….
- 4. http://www.education707.com 4 12 ÷ 2 = 6 12 ÷ 3 = 4 12 ÷ 6 = 2 12 can be divided by 2, 4 and 6 so 12 is not a prime number. 7 ÷ 7 = 1 7 ÷ 1 = 7 7 can only be divided by itself and 1 to give an integer answer. 7 is a prime number Prime numbers
- 5. http://www.education707.com 5 Copy the table below and circle the prime numbers between 1 and 40. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ex Soln. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
- 6. http://www.education707.com 6 Prime factors Defn. Prime factors are those factors of a number which are prime numbers. 30 = 2 × 3 × 5 24 = 2 × 2 × 2 × 3 = 23 × 3 Index notation 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5 Index notation 30 2 15 3 5 5 1 24 2 12 2 6 2 3 3 1 Ex. Find the prime factorisation of (a) 30 (b) 24 (c) 60 (a) (b) (c) Soln.
- 7. http://www.education707.com 7 Highest Common Factor H.C.F H.C.F Defn. The H.C.F of two or more numbers is the largest common factor among the common factors of the numbers. Ex 1. Find the H.C.F of 12 and 18. Soln. 12 = 2 × 2 × 3 18 = 2 × 3 × 3 H.C.F = 2 × 3 = 6 Select common factors
- 8. http://www.education707.com 8 Highest Common Factor H.C.F Ex 2. Find the H.C.F of 24 , 32 , 36. Soln. 24 = 2 × 2 × 2 × 3 32 = 2 × 2 × 2 × 2 × 2 H.C.F = 2 × 2 = 4 36 = 2 × 2 × 3 × 3 Step 2. Select factors common to 24, 32 and 36 Step 1. Find the prime factorisation of 24, 32 and 36 .
- 9. http://www.education707.com 9 Multiples Multiples of 2 are 2 , 4 , 6 , 8 , 10 , 12 , ……… Multiples of 3 are 3 , 6 , 9 , 12 , 15 , 18 , …….. Ex 1. Ex 2. Evaluation List the multiples of 4. List the multiples of 5. Ex 3. Ex 4.
- 10. http://www.education707.com 10 Least Common Multiple L.C.M L.C.M Defn. The L.C.M of two or more numbers is the smallest common multiple of the numbers. Ex 1. Find the L.C.M of 12 and 18. Soln. 12 = 2 × 2 × 3 18 = 2 × 3 × 3 L.C.M = 2 × 2 × 3 × 3 = 36 Find the prime factorisation of 12 and 18.