WORKSHEET ON DIVISIBILITY RULES

Detailed Solution

Problem 1 :

26 is divisible by 2.

Solution :

Given number = 26

Rule to check if the given number is divisible by 2 :

Considering the last digit of the given number, it is 2. Since it is even, 26 is divisible by 2. So, the given is true.

Problem 2 :

5221 is divisible by 5.

Solution :

Given number = 5221

Rule to check if the given number is divisible by 5 :

Considering the given number, its last digit is not 0 or 5. Then the given number is not divisible by 5. So, the given is false.

Problem 3 :

127 is divisible by 3

Solution :

Given number = 127

Rule to check if the given number is divisible by 3 :

Considering the given number, finding the sum of the digits,

= 1 + 2 + 7

= 10

Since 10 is not divisible by 3, the given number is also not divisible by 3.

So, the given statement is false.

Problem 4 :

1010 is divisible by 10

Solution :

Given number = 1010

Rule to check if the given number is divisible by 10 :

Considering the given number, the last digit of the given number is 0. Then the given number is divisible by 10.

So, the given statement is true.

Problem 5 :

1900 is divisible by 4

Solution :

Given number = 1900

Rule to check if the given number is divisible by 10 :

Considering the given number, the last digit of the given number is 0. Then the given number is divisible by 10.

Problem 6 :

1326 is divisible by 3

Solution :

Given number = 1326

Rule to check if the given number is divisible by 3 :

Let us find the sum of the digits in the given number,

= 1+ 3 + 2 + 6

= 12

Since 12 is divisible by 3, then 1326 is also divisible by 3. Then the given statement is true.

Problem 7 :

111 is divisible by 2

Solution :

Given number = 111

Rule to check if the given number is divisible by 2 :

The given number ends with 1, it is not an even number. Then it is not divisible by 2.

Problem 8 :

166 is divisible by 9

Solution :

Given number = 166

Rule to check if the given number is divisible by 9 :

Finding the sum of the digits,

= 1 + 6 + 6

= 13

This is not multiple of 9, then the given number 166 is not divisible by 9.

Problem 9 :

9288 is divisible by 9

Solution :

Given number = 9288

Rule to check if the given number is divisible by 9 :

Finding the sum of the digits,

= 9 + 2 + 8 + 8

= 27

This is multiple of 9, then the given number 9288 is divisible by 9. The given statement is true.

Problem 10 :

247 is divisible by 11

Solution :

Given number = 247

Rule to check if the given number is divisible by 11 :

Finding the sum of the digits in odd places,

= 2 + 7

= 9

Finding the sum of the digits in even places,

= 4

Difference between odd and even places = 9 - 4

= 5

So, the given statement is not divisible by 11.

Problem 11 :

5922 is divisible by 6

Solution :

Given number = 5922

Rule to check if the given number is divisible by 6 :

Since the given number ends with 2, it is even number. Then it is divisible by 2.

The sum of the digits in the given number is = 5 + 9 + 2 + 2

= 18

It is divisible by 3.

5922 is divisible by 2 and 3, then it is also divisible by 6. Then the given statement is true.

Problem 12 :

5071 is divisible by 11

Solution :

Given number = 5071

Rule to check if the given number is divisible by 11 :

Sum of the digits in the odd places = 5 + 7

= 12

Sum of the digits in the even places = 0 + 1

= 1

Difference between the digits = 12 - 1

= 11

Since the difference is multiple of 11, the given number is 5071 is also divisible by 11.  The given statement is true.

Problem 13 :

Simone's teacher told that 1738 is divisible by 11. Simone noticed that reversing the digits of this number gives 8371, which is also divisible by 11.

Explain why, if the given number is divisible by 11 and reverse its digits the result is also divisible by 11.

Solution :

Given number = 1738

Sum of digits in the odd places = 1 + 3

= 4

Sum of the digits in the even places = 7 + 8

= 15

Difference between them = 15 - 4

= 11

Since it is multiple of 11, the given number 1738 is divisible by 11. Even we are reversing the digits, the numbers occupying odd and even positions will never change. Then it is also divisible by 11.