WORKSHEET ON FACTORS AND MULTIPLES

1)  Write three multiples of 7.

2)  Find the number of factors of 75600. 

3)  Find the number of different factors of 75600. 

4)  Is 152328 the multiple of 4 ?

5)  Is 8520 the multiple of 12 ?

6)  How many factors of 2⁵ x 3⁶ x 5² are perfect squares?

a) 18    b) 24     c) 36    d) 8

7)  Write the next four multiples of the first number in each case:

(a) 5, 10, 15, .........

(b) 7, 14, 21, ...........

(c) 10, 20, 30, .............

(d) 15, 30, 45, ..............

(e) 12, 24, 36, .............

8)  Complete the following:

(a) 4th multiple of 5 is

(b) 5th multiple of 3 is

(c) 7th multiple of 8 is

(d) 6th multiple of 2 is

(e) 3rd multiple of 12 is

?

Detailed Answer Key

1. Answer : 

7 x 2  =  14

7 x 3  =  21

7 x 4  =  28

2. Answer : 

To find the number of factors that 75600 has, first we have to write 75600 in terms of its prime factors. 

Then, we have

75600  =  2⁴ ⋅ 5² ⋅ 3³ ⋅ 7¹

The exponents of the prime factors are

4, 2, 3, 1

To find the number of factors, add 1 to each of the above exponents and multiply them all. 

So, the number of factors of 75600 is 

=  (4 + 1) ⋅ (2 + 1) ⋅ (3 + 1) ⋅ (1 + 1)

=  5 ⋅ 3 ⋅ 4 ⋅ 2

=  120

Note :

These 120 factors of 75600 include 1 and 75600 also. 

3. Answer : 

In problem no. 2, already we have found the number factors of 75600.

That is 120.

These 120 factors include 1 and 75600 also as factors. 

Because the question targets the number of different factors of 75600, we have to exclude the factor 75600 from those 120 factors. 

Then, the number of different factors of 75600 is 

=  120 - 1

=  119

4. Answer :

If 152328 is the multiple of 4, then 152328 has to be exactly divisible by 4.  

So, let us verify whether 152328 is exactly divisible by 4. 

We already know that if the last two digits of the given number are zeroes or the number formed by the last two digits is a divisible by 4, then the given number is divisible by 4.  

In the given number 152328, the number formed by last two digits is 28 which is divisible by 4.

So, the number 152328 is divisible by 4 exactly. 

152328 is the multiple of 4. 

5. Answer :

If 8520 is the multiple of 12, then 8520 has to be exactly divisible by 12.  

So, let us verify whether 8520 is exactly divisible by 12.

We know that if the given number is divisible by both 3 and 4, then it is divisible by 12.

So, let us check whether the given number is divisible by 3.

Sum of the digits :

8 + 5 + 2 + 0  =  15.

Sum of the digits (15) is a multiple of 3.

So, the given number is divisible by 3. 

Now, let us check whether the given number is divisible by 4.

In the given number 8520, the number formed by the last two digits is 20 which is divisible by 4. 

So, the number 8520 is divisible by 4. 

Now, it is clear that the given number 8520 is divisible by both 3 and 4. 

So, the number 8520 is divisible by 12. 

8520 is the multiple of 12. 

6. Answer :

 2⁵ x 3⁶ x 5²

=  2⁴ x 3⁴ x 5² x 2 x 3²

• 3² is a factor and it is a perfect square.
• 2⁴ is a factor and it is a perfect square.
• 3⁴ is a factor and it is a perfect square.
• 5² is a factor and it is a perfect square.

Like wise, we get

Any factor of this number should be of the form

2^a × 3^b × 5^c

For the factor to be a perfect square a, b, c have to be even. a can take values 0, 2, 4, b can take values 0, 2, 4, 6 and c can take values 0, 2

Total number of perfect squares =3 × 4 × 2 = 24

7. Answer :

Write the next four multiples of the first number in each case:

(a) 5, 10, 15, .........

The next four multiples are :

20, 25, 30, 35

(b) 7, 14, 21, ...........

The next four multiples are :

28, 35, 42, 49

(c) 10, 20, 30, .............

The next four multiples are :

40, 50, 60, 70

(d) 15, 30, 45, ..............

The next four multiples are :

60, 75, 90, 105

(e) 12, 24, 36, .............

The next four multiples are :

48, 60, 72, 84

8. Answer :

8)  Complete the following:

(a) 4th multiple of 5 is

4 x 5 ==> 20

(b) 5th multiple of 3 is

5 x 3 ==> 15

(c) 7th multiple of 8 is

7 x 8 ==> 56

(d) 6th multiple of 2 is

6 x 2 ==> 12

(e) 3rd multiple of 12 is

3 x 12 ==> 36

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