DIVISIBILITY RULE FOR 18

If a number is divisible by both 2 and 9, then it is divisible by 18.

Example 1 :

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. 

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. 

Example 2 :

Check whether 729 is divisible by 18.

Solution :

We know that if the given 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 729 is not an even number. 

So, 729 is divisible by 2.

Because the given number 729 is not divisible by 2, it is not divisible by 18. 

Example 3 :

Check whether 54810 is divisible by 18 or not.

Solution :

We know that 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 54810 is an even number.

So, it is divisible by 2

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

Sum of the digits : 

5 + 4 + 8 + 1 + 0  =  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 54810 is divisible by both 2 and 9. 

Therefore, the number 54810 is divisible by 18. 

Example 4 :

Which of the following numbers should be multiplied by 30 to make a number divisible by 18 ?

(A)  1,  (B)  2,  (C)  3

Solution :

1 ⋅ 30  =  30

2 ⋅ 30  =  60

3 ⋅ 30  =  90

In the above calculation, when we multiply 3 by 30, we get 90 which is divisible by both 2 and 9. 

Because 90 is divisible by both 2 and 9, it is divisible by 18. 

So, option C is correct. 

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