# Formula Sheets for General Aptitude (Part A): Remainder Theorem, Download PDF!

By Renuka Miglani|Updated : March 20th, 2023

General Aptitude Formula Sheets: During the preparation, the candidates study different formulas to solve problems, but at the last moment, these formulas might not be remembered by the candidates due to exam fear or pressure. We at BYJU'S Exam Prep do not want our students to lag anywhere during the preparation, so we have come up with a concept of a Formula Sheet that will help them revise the important formulas at the last moment. This formula sheet will be a short revision tool and contain only important formulas that need to be studied at the last minute to boost the score. Our experienced subject-matter experts have meticulously designed this CSIR NET General Aptitude Formula Sheet to provide you with the best authentic material.

In this article, we will cover the CSIR NET General Aptitude Most Important Formulas of Remainder Theorem. Aspiring candidates can check all the most important formulas of the Remainder Theorem for the last-minute revision. Scroll down the full article to find out!

## Formula Sheet On Remainder Theorem

Any number can be written in the form given below:

Dividend=Divisor x Quotient + Remainder

So When 86 is divided by 10 it can be written in the form

86 = 10 x 8 + 6

Consider the following question:

17 × 23

Suppose you have to find the remainder of this expression when divided by 12.

We can write this as:

17×23 = (12+5) × (12+11)

You will realise that, when this expression is divided by 12, the remainder will only depend on the last term above:

This is the remainder when 17 × 23 is divided by 12.

Learning Point: In order to find the remainder of 17 × 23 when divide by 12, you need to look at the individual remainders of 17 and 23 when divided by 12 and then successively divide by 12 to find the remainder of the original expression Mathematically, this can be written as:

The remainder of the expression [A × B × C + D × E]/M, will be the same as the remainder of the expression [AR × BR × CR × ER]/M.

When AR is the remainder when A is divided by M,

BR is the remainder when B is divided by M,

CR is the remainder when C is divided by M

DR is the remainder when D is divided by M and

ER is the remainder when E is divided by M,

We call this transformation as the remainder theorem transformation and denote it by the sign    R→

Thus, the remainder of

USING NEGATIVE REMAINDERS

Consider the following question.

Find the remainder when: 14 × 15 is divided by 8.

The obvious approach, in this case, would be

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