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
To Get Access to Download Complete Formula Sheets on HCF And LCM, Click on The Link Below -
Download Pdf for Formula Sheet: Remainder Theorem
Check Out:
- Previous Year's Papers for CSIR-NET Exam: Attempt Here
- Study Notes for Part A: General Aptitude - Download PDF Here
- Study Notes for CSIR-NET Chemical Science - Download PDF Here
- Study Notes for CSIR-NET Life Science - Download PDF Here
More from us:
Get Unlimited access to Structured Live Courses and Mock Tests - Online Classroom Program
Get Unlimited Access to CSIR NET Test Series
~ We hope you understood the above article. Kindly UPVOTE this article and Share it with your friends.
Stay Tuned for More Such Articles !!
BYJU'S Exam Prep Team
Download the BYJU’S Exam Prep App Now.
The Most Comprehensive Exam Prep App.
#DreamStriveSucceed
App Link: https://byjusexamprep.onelink.me/iltZ
Comments
write a comment