Whole Number Arithmetic

Factors and Primes

Exercise 5 - Oral examples

{ factors of 15 }

{ factors of 32 }

{ factors of 27 }

{ factors of 28 }

(1, 3, 5, 15)

(1, 2, 4, 8, 16, 32)

(1, 3, 9, 27)

(1, 2, 4, 7, 14, 28)

Exercise 5 - Written examples

1) { factors of 4 }2) { factors of 9 }3) { factors of 16 }4) { factors of 25 }5) { factors of 36 } 6) { factors of 1 } 7) { factors of 6 } 8) { factors of 12}

• (1, 2, 4)• (1, 3, 9)• (1, 2, 4, 8, 16)• (1, 5, 25)• (1, 2, 3, 4, 6, 9, 12, 18, 36)

• (1)• (1, 2, 3, 6)• (1, 2, 3, 4, 6, 12)

Exercise 5 - Written examples

9) { factors of 18 }10) { factors of 24 }11) { factors of 10 }12) { factors of 20 }13) { factors of 30 } 14) { factors of 40 } 15) { factors of 2 } 16) { factors of 3}

• (1, 2, 3, 6, 9, 18)• (1, 2, 3, 4, 6, 8, 12, 24)

• (1, 2, 5, 10)• (1, 2, 4, 5, 10, 20)• (1, 2, 3, 5, 6, 10, 15, 30)• (1, 2, 4, 5, 8, 10, 20, 40)

• (1, 2,)• (1, 3)

Exercise 5 - Written examples

17) { factors of 5 }18) { factors of 7}19) { factors of 11 }20) { factors of 13 }

• (1, 5)• (1, 7)• (1, 11)• (1, 13)

Prime Numbers

1) Prime numbers have exactly 2 factors ( namely 1 and itself).2)If a factor is a prime number then it is called a prime factor.

{ factors of 100 } = {1, 2, 4, 5, 10, 20, 25, 50, 100 }

{ prime factors of 100 } = { 2, 5 }

Prime Numbers

• The number 1 is not a prime number and so it is not a prime factor of any number.

Exercise 5 - Written examples

21) { prime numbers between 0 and 10 }

22) { prime numbers between 10 and 20 }

23) { prime numbers between 20 and 30 }

24) { prime numbers between 30 and 40 }

• (2, 3, 5, 7)

• (11, 13, 17, 19)

• (23, 29)

• (31, 37)

25) { prime factors of 6 }

Factors of ‘6’ are 1, 2, 3, 6

Prime factors of ‘6’ are 2, 3

26) { prime factors of 10 }

Factors of ‘10’ are 1, 2, 5, 10

Prime factors of ‘10’ are 2, 5

27) { prime factors of 14 }

Factors of ‘14’ are 1, 2, 7, 14

Prime factors of ‘14’ are 2, 7

28) { prime factors of 15 }

Factors of ‘15’ are 1, 3, 5, 15

Prime factors of ‘15’ are 3, 5

29) { prime factors of 21 }

Factors of ‘21’ are 1, 3, 7, 21

Prime factors of ‘21’ are 3, 7

30) { prime factors of 35 }

Factors of ‘35’ are 1, 5, 7, 35

Prime factors of ‘35’ are 5, 7

31) { prime factors of 30 }

Factors of ‘30’ are 1, 3, 5, 6, 10, 30

Prime factors of ‘30’ are 3, 5

32) { prime factors of 42 }

Factors of ‘42’ are 1, 2, 3, 6, 7, 14, 21, 42

Prime factors of ‘42’ are 2, 3, 7

Multiples

33) { multiples of 3 }

34) { multiples of 6 }

35) { multiples of 2 }

36) { multiples of 4 }

• 3, 6, 9, 12, …• 6, 12, 18, 24,,…• 2, 4, 6, 8, …• 4, 8, 12, 16, …

41) { factors of 60 }

42) { factors of 360 }

43) { prime numbers between 40 and 50 }

44) { prime numbers between 50 and 60 }

• (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)

• (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360)

• (41, 43, 47)• (53, 59)

Exercise 6 - Prime factors42

6 7

Prime factors42

6 7

‘7’ is a prime number

Prime factors42

6 7

2 3

2, 3, and 7 are all prime numbers

Product of prime factors42

6 7

2 3

Exercise 6 - Prime factors28

4 7

Prime factors28

4 7

‘7’ is a prime number

Prime factors28

4 7

2 2

2, and 7 are all prime numbers

Product of prime factors28

4 7

2 2

Exercise 6 - Prime factors64

8 8

Prime factors64

8 8

2 4 2 4

Prime factors64

8 8

2 4 2 4

2 2 2 2

Product of Prime factors64

8 8

2 4 2 4

2 2 2 2

Exercise 6 - Prime factors72

8 9

Prime factors72

8 9

2 4 3 3

Prime factors72

8 9

2 4 3 3

2 2

Product of Prime factors72

8 9

2 4 3 3

2 2

Exercise 6Write these numbers as products of their primes

1) 6

2) 10

3) 14

4) 15

5) 21

6) 35

7) 30

8) 70

• 2 x 3• 2 x 5• 2 x 7• 3 x 5• 3 x 7• 5 x 7• 2 x 3 x 5• 2 x 5 x 7

Exercise 6

9) 4

10) 8

11) 16

12) 32

13) 9

14) 27

15) 25

16) 49

• 2 x 2 = 22

• 2 x 2 x 2 = 23

• 2 x 2 x 2 x 2 = 24 • 25

• 3 x 3 = 32

• 3 x 3 x 3 = 33

• 5 x 5 = 52

• 7 x 7 = 72

Exercise 6

17) 12

18) 18

19) 20

20) 50

21) 45

22) 75

23) 36

24) 60

• 2 x 2 x 3 = 22 x 3• 2 x 3 x 3 = 2 x 32

• 2 x 2 x 5 = 22 x 5 • 2 x 5 x 5 =2 x 52

• 5 x 3 x 3 = 5 x 32

• 3 x 5 x 5 = 3 x 52

• 2 x 2 x 3 x 3 = 22 x 32

• 2 x 2 x 3 x 5 = 22 x 3 x 5

Exercise 6

25) 24

26) 54

27) 40

28) 56

29) 48

30) 80

31) 90

32) 84

• 23 x 3• 2 x 33

• 23 x 5 • 7 x 23

• 24 x 3• 24 x 5• 2 x 32 x 5• 22 x 3 x 7

Exercise 6

33) Find the smallest number which is the product of 4 different prime factors.

• 2 x 3 x 5 x 7 = 210

Exercise 6 - 34

• Find the next smallest number which is the product of 4 different prime factors.

• 2 x 3 x 5 x 11 = 330

Exercise 6 - 35

Find the smallest number which is the product of 4 prime factors (not necessarily different).

• 2 x 2 x 2 x 2 = 16

Exercise 6 - 36

Find the next smallest number which is the product of 4 prime factors (not necessarily different).

• 2 x 2 x 2 x 3 = 24