Divisibility Rules

Given a number $x$, can you determine if it is divisible by a number say $y$ with out even performing the actual division. Divisibility rules are quite handy when you want to test for divisibility of numbers even before you can actual divide the number. For instance, to check if a number is divisible by 7, […]

Remainders of Large Numbers using Fermat’s and Euler’s Theorem

To understand the basics of calculating remainders like the sum and product of remainders, concept of negative remainders etc click here – Remainders Basics In this post we will see how to find the remainders of large numbers using the remainder theorems – Fermat’s Little theorem and Euler’s theorem using the Euler’s Totient function. Fermat’s Little […]

Using Chinese Remainder Theorem

A bag has certain number of pens. If you take out 3 pens at a time, 2 pens are left, if you take 4 pens, 1 pen is left and if you take 5 pens at a time, 3 pens are left in the bag. What is the smallest number of pens in the bag? […]

Least Common Multiple

In this post we explain the basics of Least Common Multiple(LCM). We will understand the techniques on how to find the LCM of two or more numbers. Under the “Problems on LCM” section we will solve some important aptitude problems on LCM. Understanding Least Common Multiple   Problems on LCM

Highest Common Factor

In this post we explain the basics of Highest Common Factor (HCF) also known as the Greatest Common Divisor(GCD) or the Greatest Common Factor(GCF). We will understand the techniques on how to find the HCF of two or more numbers. Under the “Problems on HCF” section we will solve some important aptitude problems on HCF. […]

Highest Power of a Number in a Factorial

In the video below, we will have a look at the techniques to calculate the Highest Power of a Number in a Factorial. Factorial of a number n is given by $n! = n$ x $(n-1)$ x $(n-2)$ x $(n-3)…2$ x $1$ Given a number x, how do we find the highest power of x in […]

Problems on Divisors of Number

In this post we will have a look at the problems on the number of divisors of a number. We will see how to find the number of divisors of a number, number of even and odd divisors of a number, sum of divisors of a number and product of divisors of a number. The […]

How to find Remainders – Basics

Basics of Calculating Remainders [latexpage] In this post we will have a look at the basics of calculating remainders like the remainder of a sum, remainder of a product and understand what is meant by negative remainders. We will see how to use these concepts to calculate the remainders of large numbers. What is a […]

Last Two Digits of Large Number

Here, we will see how to find the last two digits of a large number. We will first understand how to find the last two digits of a product and  then we will try to find the last two digits ( i.e digits in tens and units place) of a large number in the form ${x^y}$. At […]

Units digit of a number raised to power

Here, we will see how to find the units digit of a number that is in the form ${x^y}$. We will first try to understand what is a units digit, then we will look at the technique to find the units digit of large powers and then using this technique we will solve some problems […]