## Application of Concept of Cyclicity

Application of Concept of Cyclicity How to calculate unit digit if a number contains power of a power Example 1:What will be the last digit of ${{12}^{{{23}^{45}}}}$ Solution: To find the last digit of this type of number we will start the question from the base the...

## Remainders (Part-5)

Remainders: Part-5 In this article we will discuss calculating remainders that involve hefty mathematical expressions. We will discuss each and every mathematical expression one by one. Suppose we have two numbers “a” and “b”. If “a” is in form of 7n +4 and “b” is in...

## Remainders (Part-4)

Remainders: Part-4 In this article, for calculating remainders we will use concept of cyclicity. Let’s take an example of questions based on concept of remainders. Example Find the remainder when 47123 is divided by 7? Solution: We will do this question step by step...

## Remainders (Part-3)

Remainders: Part-3 Problem Type 1: What will be the remainder when p + q +r +… is divided by d Example What will be the remainder when 63 + 67 +81 is divided by 11 ? Solution: Instead we add up all numbers, lets do it separately 63 when divided by 11 gives 5 as...

## Extra Problems for ‘Number of Zeros’ Question Type

Extra Problems for ‘Number of Zeros’ Question Type Example 1: Find the number of zeros in 2145 x 5234  . Solution:When we see the question it looks like a very difficult question but this type of question involving number of zeros is very simple and can be solved in...

## Number of zeros at the end of a factorial

Number of zeros at the end of a Problem Type: Number of zeros at the end of p! To solve such type of problems we see only pair of 2 x5 in p! . Because if a number is divisible by 10 then it will have 0 in the end and 10= 2×5 so finding number of zeros is...  