NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

CHAPTER 12

Numbers, Quantification and Numerical Application

CHAPTER AT A GLANCE

Modular Arithmetic

A system of arithmetic for integers, which deals with remainders only, is known as Modular Arithmetic.

We have learnt Euclid’s division algorithm in previous classes. It states that:

Dividend = Divisor × Quotient + Remainder

Given two positive integers X and Y such that X > Y and Y ≠ 0 then

X = Y × Q + R

Where, X = Dividend

Y = Divisor

Q = Quotient

R = Remainder, 0 ≤ R < Y

Modulo Operator

Given two integers X and Y; X > Y and Y ≠ 0

X = Y × Q + R

where 0 ≤ R < Y

Then there exist two unique integers Q and R such that the same expression can be written as:

X mod Y = R…(i)

Where mod (modulo) gives the remainder after X is divided by