Number System - Divisibility questions are asked in Most of the competitive and Entrance examinations including SSC, IBPS, TET and others. These Divisibility questions are asked in number system in quantitative aptitude or math section. These questions are one of the most difficult and time consuming for candidates who had not solved them before. But the difficulty of these Divisibility questions in Number System can be eased with the help of shortcut tricks which I am going to mention here.
Suppose you are given a Number System-Divisibility question like below one.
Example Question 1: Determine the remainder when 24^81 is divided by 23?      (^ means power)
Solution with Number System - Divisibility Shortcut trick:
To solve the question, first divide 24 by 23. The remainder is 1.
Now you have (1)^81 which equals 1. So the remainder is 1. Ans.

Important Note of Number System - Divisibility Shortcut trick: You have to convert Numerator to 1 or -1 value by dividing it with denominator. We have applied this formula in the above and below questions.

Example Question 2:
Determine the remainder when 2^24 is divided by 7?
Easy Solution of this Number system problem with Divisibility Shortcut trick:
Given (2^24)/7
Now convert we have to convert the numerator to 1 or -1 in relation to denominator.
So convert (2^24)/7 to [(2^3)^21]/7
So that it becomes (8^21)/7
Now when you divide 8 by 7, the remainder is 1.
So we get 1^21 which equals 1.
So the remainder is 1. Ans.
Let us take another example to better understand this Number System - divisibility shortcut trick.
Example 3. What is the remainder when 51^202 is divided by 7.
Here is Easy shortcut for this Number System -  divisibility question.
Divide 51 by 7. The remainder is 2.
So we have (2^202)/7
Which equals [(2^3)^67x (2^1)]/7
Since 2^3 equal 8. Dividing it with 7, we get remainder 1.
So it becomes [(1^67)x2]/7
1^67 equals 1. Multiplying it with 2, we get 2.
So we get 2/7. So the remainder is 2.
Note: When a small numerator is divided by large denominator, the remainder is always that numerator i.e. for 1/7, the remainder is 1.
For 3/7, the remainder is 3. For 5/9, the remainder is 5.
So these are the Number System - divisibility shortcut tricks. More tricks will be posted on other types of Divisibility questions if this post is shared well. So share this post with your friends so that we can post some other types of shortcut tricks for divisibility questions and other shortcut tricks.