## DIVISIBILITY RULES WORKSHEET

Problem 1 :

Check whether 16 is divisible by 2.

Problem 2 :

Check whether 252 is divisible by 3.

Problem 3 :

Check whether 328 is divisible by 4.

Problem 4 :

Check whether 105 is divisible by 5.

Problem 5 :

Check whether 5832 is divisible by 6.

Problem 6 :

Check whether 504 is divisible by 7.

Problem 7 :

Check whether 4328 is divisible by 8.

Problem 8 :

Check whether 9477 is divisible by 9.

Problem 9 :

Check whether 9470 is divisible by 10.

Problem 10 :

Check whether 762498 is divisible by 11.

Problem 11 :

Check whether 8520 is divisible by 12.

Problem 12 :

Check whether the number 41295 is divisible by 15.

Problem 13 :

Check whether 1458 is divisible by 18.

Problem 14 :

Check 3500 is divisible by 25.

Problem 1 :

Check whether 16 is divisible by 2.

Solution :

According to the divisibility rule for 2, all even numbers are divisible by 2.

A number ends with one of the following digits is called as even number.

0, 2, 4, 6 or 8

The given number 16 ends with the digit 6.

So, 16 is an even number and it is divisible by 2.

Problem 2 :

Check whether 252 is divisible by 3.

Solution :

According to the divisibility rule for 3, if the sum of all the digits is divisible by 3 or a multiple of 3, then the number is divisible by 3.

Add all the digits in the number 252.

2 + 5 + 2  =  9

The sum of the digits in the given number 252 is 9 which is a multiple of 3.

So, 252 is divisible by 3.

Problem 3 :

Check whether 328 is divisible by 4.

Solution :

According to the divisibility rule for 4, if the last two digits are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

In the given number 328, the last two digits are not zeroes.

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

So, the given number 328 is divisible by 4.

Problem 4 :

Check whether 105 is divisible by 5.

Solution :

According to the divisibility rule for 5, if a number ends with 0 or 5, then it is divisible by 5.

The given number 105 ends with 5.

So, the given number 105 is divisible by 5.

Problem 5 :

Check whether 5832 is divisible by 6.

Solution :

According to the divisibility rule for 6, if a number is divisible by both 2 and 3, then it is divisible by 6.

The given number 5832 ends with 2.

So, it is an even number and divisible by 2.

Check whether the number 5832 is divisible by 3.

5 + 8 + 3 + 2  =  18

The sum of the digits in the given number 5832 is 18 which is a multiple of 3.

Therefore, the given number 5832 is divisible by both 2 and 3.

So, the given number 5832 is divisible by 6.

Problem 6 :

Check whether 504 is divisible by 7.

Solution :

According to the divisibility rule for 7, in a number, if the difference between twice the digit in one's place and the number formed by other digits is either zero or a multiple of 7, then the number is divisible by 7.

In the given number 504, twice the digit in one's place is

=  2 ⋅ 4

=  8

The number formed by the digits except the digit in one's place is

=  50

The difference between twice the digit in one's place and the number formed by the other digits is

=  50 - 8

=  42

42 is divisible by 7.

So, the given number 504 is divisible by 7.

Problem 7 :

Check whether 4328 is divisible by 8.

Solution :

According to the divisibility rule for 8, in a number, if the last three digits are zeros or the number formed by the last 3 digits is divisible by 8, then the number is divisible by 8.

In the given number 4328, the last three digits are not zeroes.

But, the number formed by the last three digits is 328 which is divisible by 8.

So, the given number 4328 is divisible by 8.

Problem 8 :

Check whether 9477 is divisible by 9.

Solution :

According to the divisibility rule for 9, if the sum of the digits in a number is divisible by 9 or multiple of 9, then the number is divisible by 9.

Add all the digits in the number 9477.

9 + 4 + 7 + 7  =  27

The sum of the digits in the given number 9477 is 9 which is divisible by 9.

So, 9477 is divisible by 9.

Problem 9 :

Check whether 9470 is divisible by 10.

Solution :

According to the divisibility rule for 10, if a number ends with 0, then it is divisible by 10.

The number 9470 ends with 0.

So, it is divisible by 10.

Problem 10 :

Check whether 762498 is divisible by 11.

Solution :

According to the divisibility rule for 11, in a number, if the sum of the digits in odd places and sum of the digits in even places differ by zero or a number divisible by 11, then the given number is divisible by 11.

In the given number 762498,

Sum of the digits in odd places  =  7 + 2 + 9

Sum of the digits in odd places  =  18

In the given number 762498,

Sum of the digits in even places  =  6 + 4 + 8

Sum of the digits in even places  =  18

The difference between the sum of the digits in odd places and sum of the digits in even places is

=  18 - 18

=  0

Sum of the digits in odd places and sum of the digits in even places differ by zero.

So the given number 762498 is divisible by 11.

Problem 11 :

Check whether 8520 is divisible by 12.

Solution :

According to the divisibility rule for 12, if a number is divisible by both 3 and 4, then it is divisible by 12.

First, check whether the given number 8520 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, 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.

Therefore, the number 8520 is divisible by 12.

Problem 12 :

Check whether the number 41295 is divisible by 15.

Solution :

According to the divisibility rule, if a number is divisible by both 3 and 5, then it is divisible by 15.

First, 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, 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.

Therefore, the number 41295 is divisible by 15.

Problem 13 :

Check whether 1458 is divisible by 18.

Solution :

According to the divisible rule for 18, if a number is divisible by both 2 and 9, then it is divisible by 18.

First, check whether the given number is divisible by 2.

The given number 1458 is an even number.

So, it is divisible by 2

Now, 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.

Therefore, the number 1458 is divisible by 18.

Problem 14 :

Check 3500 is divisible by 25.

Solution :

According to the divisible rule for 25, in a number, if the last two digits are zeroes or the number formed by the last two digits is a multiple of 25, then the number is divisible by 25.

In the given number 2800, the last two digits are zeroes.

So, the number 2800 is divisible by 25.

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