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FACTORS &

MULTIPLESR.USHAR.USHA

TGT ( MATHEMATICS)TGT ( MATHEMATICS)KV,GILL NAGARKV,GILL NAGAR

CHENNAI.CHENNAI.

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22

ARRANGEMENT OF STARS

Take 6 stars and arrange

them in different

ways

33

1 Row × 6 Stars/Row = 6 Stars

44

3 Rows × 2 Stars per row = 6 stars

55

22 Rows Rows × × 33 stars per row = stars per row = 66 stars stars

66

6 Rows × 1 Star/Row = 6 Stars

77

As we can see, 6 can be written as product of two numbers in many ways: 6 = 1 × 6

6 = 2 × 3

6 = 3 × 2

6 = 6 × 1

1, 2, 3 and 6 are exact divisors of 6

8

ARRANGEMENT OF FOOTBALLS

Take 8 footballs and arrange

them in different

ways

99

Arrangement of 8 in different ways

1 Row × 8 Balls/Row = 8 Balls

1010

2 Rows × 4 Balls / Row = 8 Balls

1111

4 Rows ×

2 Balls / Row =

8 Balls

1212

8 Rows × 1 Ball / Row =

8 Balls

1313

1, 2, 4 and 8 are exact divisors of 8.

14

7 divides 28 exactly and gives Quotient 4 and

Remainder 0.

28 ÷ 7 = 4

15

4 divides 28 exactly and gives Quotient 7 and

Remainder 0.

28 ÷ 4 = 7

16

28 divides 28 exactly and gives Quotient 1 and Remainder 0.

28 ÷ 28 = 1

17

28 ÷ 1 = 28

28 ÷ 4 = 7

28 ÷ 7 = 4

28 ÷ 28= 1

1

4

7

28

FACTORS OF 28

18

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 4 = 4

16 ÷ 8 = 2

16 ÷ 16 = 1

1

2

4

8

16

FACTORS OF 16

19

FACTOR

A factor of a number is an exact

divisor of that number i.e. the factor

leaves remainder 0 when it divides

the number.

20

4 × 5 = 20

4 and 5 are factors of 20. We can also say that 20 is multiple of 4 and 5.

In 2 × 12 = 24,

2 and 12 are factors of 24.

24 is the multiple of 2 and 12.

So, a number is a multiple of its factors.

21

Multiples of 2 = 2,4,6,8,10,12,14,16,18,20,22,24…

Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,33,36,…

Multiples of 15 = 15,30,4,60,75,90,105,120,135,……

The number of multiples of a given number is infinite.

22

FACTORS OF SOME NUMBERS

8 = 1,2,4,8

16 = 1,2,4,8,16

25 = 1,5,25

23

4 × 5 = 20

Factors Multiple

24

POINTS TO REMEMBER

• 1 is a factor of every number.

• Every factor of a number is an exact divisor of that number.

• Every factor is less than or equal to the given number.

• Number of factors of a given number are finite.

25

• Every multiple of a number is greater than or equal to that number.

• The number of multiples of a given number is infinite.

• Every number is a multiple of itself.

POINTS TO REMEMBER contd

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FACTOR OR MULTIPLE?FACTOR OR MULTIPLE? For each of numbers in the statements, select For each of numbers in the statements, select

either multiple [M] or factor [F]either multiple [M] or factor [F] 34 34 × 5 = 170× 5 = 170 [[FF] [] [MM] [] [FF] [] [MM] [] [FF] [] [MM]]

25 × 4 = 10025 × 4 = 100 [[FF] [] [MM] [] [FF] [] [MM] [] [FF] [] [MM]]

90 × 10 = 90090 × 10 = 900 [[FF] [] [MM] [] [FF] [] [MM] [] [FF] [] [MM]]

45 × 6 = 27045 × 6 = 270 [[FF] [] [MM] [] [FF] [] [MM] [] [FF] [] [MM]]

7 × 30 = 2107 × 30 = 210 [[FF] [] [MM] [] [FF] [] [MM] [] [FF] [] [MM]]

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State whether the following State whether the following statements are statements are TRUETRUE or or FALSEFALSE

1. 1 is a factor of every number. 1. 1 is a factor of every number. FF TT2. The largest factor of any number is the number itself. 2. The largest factor of any number is the number itself. FF TT3. Number of factors of a given number is infinite. 3. Number of factors of a given number is infinite. FF TT4.The number of multiples of 5 is 10. 4.The number of multiples of 5 is 10. FF TT5.The factors of 65 are 1, 5 and 13 only. 5.The factors of 65 are 1, 5 and 13 only. FF TT

( Click ‘F’ for false and ‘T’ for true )( Click ‘F’ for false and ‘T’ for true )

2828

THANK YOU

2929

CORRECTCORRECT

3030

WRONGWRONG