DIVISIBILITY RULES WORKSHEET

About "Divisibility Rules"

Divisibility Rules Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on divisibility rules. 

Before look at the worksheet, if you wish to learn divisibility rules in detail, please click here

Divisibility Rules Worksheet - Problems

1.  Check whether 16 is divisible by 2. 

2.  Check whether 252 is divisible by 3.

3.  Check whether 328 is divisible by 4.

4.  Check whether 105 is divisible by 5.

5.  Check whether 5832 is divisible by 6. 

6.  Check whether 998 is divisible by 9.

7.  Check whether 9470 is divisible by 10. 

8.  Check whether 198 is divisible by 11.

9.  Check whether 8520 is divisible by 12 or not.

10.  Check whether the number 41295 is divisible by 15.

11.  Check whether 1458 is divisible by 18.

12.  Check 3500 is divisible by 25.

Divisibility Rules Worksheet - Solution

Problem 1 :

Check whether 16 is divisible by 2. 

Solution :

We already know that if a number is an even number, then it is divisible by 2. 

The given number 16 is an even number.  

Hence, the number 16 is divisible by 2.

Problem 2 :

Check whether 252 is divisible by 3.

Solution :

We already know that if the sum of the digits in the given number is a multiple of 3, then the given number is divisible by 3. 

Sum of the digits : 

2 + 5 + 2  =  9

Sum of the digits (9) is a multiple of 3.

Hence, the number 252 is divisible by 3. 

Problem 3 :

Check whether 328 is divisible by 4.

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

Hence, the number 328 is divisible by 4. 

Problem 4 :

Check whether 105 is divisible by 5 ?

Solution :

In the given number 185, the last digit 5.

Hence, the given number 105 is divisible by 5.

Problem 5 : 

Check whether 5832 is divisible by 6. 

Solution :

We know that if the given number is divisible by both 2 and 3, then it is divisible by 6.

So, let us check whether the given number is divisible by 2.

The given number 5832 is an even number.

So it is divisible by 2. 

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

Sum of the digits :

5 + 8 + 3 + 2  =  18

Sum of the digits (18) is a multiple of 3. 

So, the number 5832 is divisible by 3. 

Now, it is clear that the given number 5832 is divisible by both 2 and 3. 

Hence, the number 5832 is divisible by 6. 

Problem 6 : 

Check whether 998 is divisible by 9.

Solution :

We already know that if the sum of the digits in the given number is a multiple of 9, then the given number is divisible by 9. 

Sum of the digits : 

9 + 9 + 8  =  26

Sum of the digits (26) is not a multiple of 9.

Hence, the number 998 is not divisible by 9. 

Problem 7 : 

Check whether 9470 is divisible by 10. 

Solution :

Here the last digit of the given number is 0.

Hence, the given number 9470 is divisible by 10.

Let us look at the next problem on "Divisibility rules worksheet". 

Problem 8 : 

Check whether 198 is divisible by 11.

Solution :

In this three digit number, 

the sum of the first and last number = middle number.

That is 1 + 8 = 9.

So the given number 198 is divisible by 11.

Let us look at the next problem on "Divisibility rules worksheet". 

Problem 9 : 

Check whether 8520 is divisible by 12 or not.

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. 

Hence, the number 8520 is divisible by 12. 

Let us look at the next problem on "Divisibility rules worksheet". 

Problem 10 : 

Check whether the number 41295 is divisible by 15?

Solution :

We know that if a number is divisible by both 3 and 5, then it is divisible by 15. 

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

Sum of the digits :

4 + 1 + 2 + 9 + 5  =  21.

Sum of the digits (21) is a multiple of 3.

So, the given number is divisible by 3. 

Now, let us check whether the given number is divisible by 5.

In the given number 41295, the digit in one's place is 5. 

So, the number 41295 is divisible by 5. 

Now, it is clear that the given number 41295 is divisible by both 3 and 5. 

Hence, the number 41295 is divisible by 15. 

Let us look at the next problem on "Divisibility rules worksheet". 

Problem 11 :

Check whether 1458 is divisible by 18.

Solution :

We know that if a number is divisible by both 2 and 9, then it is divisible by 18. 

So, let us check whether the given number is divisible by 2.

The given number 1458 is an even number.

So, it is divisible by 2

Now, let us check whether the given number is divisible by 9.

Sum of the digits : 

1 + 4 + 5 + 8  =  18.

Sum of the digits (18) is a multiple of 9.

So, the given number is divisible by 9. 

Now, it is clear that the given number 1458 is divisible by both 2 and 9. 

Hence, the number 1458 is divisible by 18. 

Let us look at the next problem on "Divisibility rules worksheet". 

Problem 12 :

Check 3500 is divisible by 25.

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 multiple of 25, then the given number is divisible by 25.  

In the given number 3500, the last two digits are zeroes.

Hence, the number 3500 is divisible by 25.

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