Whole Number Arithmetic Highest common factor Lowest common multiple

H.C.F (highest common factor) { factors of 8 } = { 1, 2, 4, 8 } { factors of 12 } = { 1, 2, 3, 4, 6, 12 } The H.C.F. is 4

L.C.M (lowest common multiple) { multiples of 8 } = { 8, 16, 24, 32 … } { multiples of 12 } = {12, 24, 36 … } The L.C.M. is 24

2 and 6 H.C.F 2 L.C.M 6

2 and 10 H.C.F 2 L.C.M 10

3 and 6 H.C.F 3 L.C.M 6

3 and 12 H.C.F 3 L.C.M 12

4 and 12 H.C.F 4 L.C.M 12

5 and 10 H.C.F 5 L.C.M 10

4 and 6 H.C.F 2 L.C.M 12

6 and 8 H.C.F 2 L.C.M 24

6 and 9 H.C.F 3 L.C.M 18

9 and 12 H.C.F 3 L.C.M 36

4 and 10 H.C.F 2 L.C.M 20

6 and 10 H.C.F 2 L.C.M 30

2, 4 and 8 H.C.F 2 L.C.M 8

4, 6 and 8 H.C.F 2 L.C.M 24

3, 6 and 12 H.C.F 3 L.C.M 12

6, 9 and 12 H.C.F 3 L.C.M 36

Exercise 7 - Oral examples True or False 1)5 is a factor of 10. 2)5 is a multiple of 10. 3)10 is a factor of 5. 4)10 is a multiple of 5. 5)7 is a factor of 7. 6)7 is a multiple of 7. 7)7 is a prime number. 8)9 is a prime number. 9)3 is a prime factor of 12. True False True False true

Set Notation If x is an element (or member) of a set A then we write If x is not an element of a set A then we write. e.g. if A = { factors of 10 } = { 1, 2, 5, 10 } Then, Whereas.

If all the elements of A are also elements of B then we say that A is a subset of B and write e.g. If A = {prime factors of 10} = {2, 5} and B = {factors of 10} = {1, 2, 5, 10} then

Exercise 7 Choose the correct symbol 1) 2 _____ { 1, 2, 3 } 2) { 2 } ____ { 1, 2, 3 } 3) 7 ______ { 4, 5, 6 } 4) { 7 }____ { 4, 5, 6 } 5) 3 _____ { 2, 3, 4 } 6) 8 ______ { 5, 6, 7 } 7) { 3 } ____ { 2, 3, 4 } 8) { 8 } ____ { 5, 6, 7 }

Exercise 7 9) 5 ______ { factors of 5 } 10) 5 _____ { multiples of 5 } 11) 4 _______ { factors of 8 } 12) 4 ______ { multiples of 8 } 13) 6 _________ { factors of 3 } 14) 6 __________ { multiples of 3 } 15) { 5 }______ { factors of 5 } 16) { 5 } _______ { multiples of 5 }

Exercise 7 17) { 4 } ____ { factors of 8 } 18) { 4 } _____ { multiples of 8 } 19) { 6 } _____ { factors of 3 } 20) { 6 } _____ { multiples of 3 } 21) 17 ______ { prime numbers } 22) { 17 } ____ { prime numbers } 23) 27 _____ { prime numbers } 24){ 27 } ____ { prime numbers }

Exercise 7 25) 1 ____ { prime factors of 3 } 26) 2 ____ { prime factors of 6 } 27) { 3 }____ { prime factors of 9 } 28) { 4 } _____{ prime factors of 12}