DIVISIBILITY RULE FOR 12

If a number is divisible by both 3 and 4, then it is divisible by 12.

Example 1 :

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.

First, 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, 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. 

Example 2 :

Check whether 9110 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.

First, check whether the given number is divisible by 3.

Sum of the digits :

9 + 1 + 1 + 0  =  11

Sum of the digits (11) is not a multiple of 3.

So, the given number is not divisible by 3. 

Because the given number 9110 is not divisible by 3, the number 9110 is not divisible by 12. 

Example 3 :

Check whether 2340 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.

First, check whether the given number is divisible by 3.

Sum of the digits :

2 + 3 + 4 + 0  =  9

Sum of the digits (9) is not a multiple of 3.

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

In the given number 2340, the number formed by the last two digits is 40 which is divisible by 4. 

So, the number 2340 is divisible by 4. 

Now, it is clear that the given number 2340 is divisible by both 3 and 4. 

Therefore, the number 2340 is divisible by 12. 

Example 4 :

Which of the following numbers should be multiplied by 20 to make a number divisible by 12 ?

(A)  1,  (B)  2,  (C)  3

Solution :

1 ⋅ 20  =  20

2 ⋅ 20  =  40

3 ⋅ 20  =  60

In the above calculation, when we multiply 3 by 20, we get 60 which is divisible by both 3 and 4. 

Because 60 is divisible by both 3 and 4, it is divisible by 12. 

So, option C is correct. 

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