05/06/2023
Many competitive exam like SSC, Banking, Railway & CSAT ask question based on divisibility rule. Sometimes they ask to check the divisibility of 99.
So the question is "Is there a divisibility rule for 99? Does it always work?"
My answer is "YES". There is a divisibility rule for 99 and it always work.
Let's discuss that method...
The method to check divisibility of 99 by 9 and 11 are certainly correct, but there’s another way that would also work.
This method tells us that:-
Step1:- We will have to split the digits of the number into pairs ( block of 2 digit ) starting from right hand side ( from unit digit ).
Step2:- After making the pairs we will keep on adding these pairs.
Step3:- If the result is divisible by 99, then that number is also divisible by 99.
Let's take some example:-
(1) The number 15309756.
A/Q to the above rule,
First make the pair starting from right hand side,
15 30 97 56
Add these pairs:- 15+30+97+56 = 198
Have you noticed 198 is multiple of 99, i.e. 99 X 2, but if you don't figure out you can apply the above method again,
1 98
1 + 98 = 99 , so the result we got is 99 itself so the number 15309756 is divisible by 99.
Take another example,
(2) The number 4596372.
A/Q the above rule,
First make the pairs starting from right hand side,
4 59 63 72
Add these pairs:- 4+59+63+72 = 198
again we got 198 as a result and we know it is 99 X 2, so the number is divisible by 99.
NOTE:- (1) If we start with any number divisible by 99 and keep on adding the digit pairs until we get a number less than 100, it will always be 99.
(2) After applying the above method if the number doesn't happen to be divisible by 99, then this will tell us what the remainder is. it means the result we got is the remainder when that number will be divided by 99.
It will take less time than by checking 9&11.
I hope it will help you and if you have any doubt please do comment.
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