# Finding reminder of a large number

Number System is an important concept for solving GATE Aptitude questions and aptitude for entrance exams for different companies.

The below is an important question which has been asked in many exams.

Question :
In 7126 is divisible by 48, find reminder?

Normal Approach :
For calculating the reminder we first calculate the original value for number 7126 and divide it further to and obtain the reminder.
It is very long and time taking process and it is not at all feasible to solve it in this way. So we use some important mathematical concepts related to divisibility to solve this problem.

Speedy approach :
Important concepts for solving problem,

• (xn – an) divisible by (x – a) for every n (n belongs to integers)
• (xn – an) divisible by (x + a) for every even number n (n belongs to integers)
• (xn – an) divisible by (x + a) for every odd number n (n belongs to integers)

And we also use another basic formula;

`Dividend = divisor x quotient + reminder `

The given number in form such that the base is very near to 48.

This is done by using the formula ( amn ) = (am)n

`7126 = (72)63 = 4963 `

Now by using our mathematical formulae we should add or subtract a number to 4963 such that it is divisible by 48.

`(4963 – 1) = (4963 - 163) `

By comparing it with (xn – an) we can write,

`x = 49, n = 63 and a = 1`

Therefore from the above we get that
( 4963 – 163) is divisible by (49-1) and (49+1)
So, (4963 – 1) is divisible by 48
Let (4963 – 1)/48 = q (where q is the quotient )

```4963 – 1 = 48 x q
4963 = 48 x q + 1
7126 = 48 x q + 1 ```

Comparing with.

`Dividend = divisor * quotient + reminder `

So from above when Dividend = 7126, divisor = 48 then reminder is 1.
So when 7126 is divided by 48 the reminder is 1.

In this way we can obtain the reminder for such large numbers. It takes very less time and very useful in competitive exams.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.