whole number arithmetic highest common factor lowest common multiple

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 examplesTrue 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• False• True• True• True• 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 7Choose 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}