FACTORS AND DIVISORS WORKSHEET

About "Factors and Divisors Worksheet"

Factors and Divisors Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on factors and divisors. 

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Factors and Divisors Worksheet - Problems

Problem 1 : 

Write three multiples of 12.

Problem 2 : 

Find the number of factors of 75600. 

Problem 3 : 

Find the number of different factors of 75600. 

Problem 4 :

Is 4 the divisor of 5698328 ?

Problem 5 : 

Is 12 the divisor of 8520 ?

Factors and Divisors Worksheet - Solutions

Problem 1 : 

Write three multiples of 12.

Solution : 

12 x 2  =  24

12 x 3  =  36

12 x 4  =  48

Problem 2 : 

Find the number of factors of 75600. 

Solution : 

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 ⋅ 5⋅ 3⋅ 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. 

Problem 3 : 

Find the number of different factors of 75600. 

Solution : 

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

Problem 4 :

Is 4 the divisor of 5698328 ?

Solution :

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 5698328, the number formed by last two digits is 28 which is divisible by 4.

So, the number 5698328 is divisible by 4 exactly. 

Hence, 4 is the divisor of 5698328. 

Problem 5 : 

Is 12 the divisor of 8520 ?

Solution :

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. 

Hence, 12 is the divisor of 8520.

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