# Divisibility

## Concept: Remainder Theorem

Suppose you are asked to find remainder of following expression Person with average math skills will do all the calculation and come with the answer.But the Question can be easily solved using Remainder Theorem REMAINDER THEOREM In this process, you have to individually calculate each values and write the remainders This way you can easily …

## Concept: Number of Zeros in Factorial Value

CONCEPT 1 Suppose you are given a number in factorial numbers and you are asked to find number of zeros possible in that factorial. In questions involving number of zeros, you have to find the possible combination of (2 * 5) For example:Find number of zeros in 6! 6! can be written as 6 ! …

## Concept: Number of Zeroes in Expression

The number of zero’s in any expression depends on number of combination of (2 *5) present in that expression.Hence zeros are formed by the combination of 2 & 5 For Example; Suppose you are asked to find number of zeros in following expression8 * 15 * 23 * 17 * 25 * 22 Step 1: …

## Divisibility Question : Finding sum of Factors

Question 01 For the number 2450, find the sum of all factors Step 1: Factor representation Step 2: Sum of factors can be written as Solving the equation we get = 3 * 31* 57 = 5301Hence, sum of all the factors is 5301

## Questions : Highest power in Factorial

Calculate the highest power of 5 in 10! Let’s see how layman will solve this question 10! can be written as:10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1Now you have to look for numbers which contain 5 (i.e. that ends with 5 …

## Questions : Find number of Zeros

Question 01 Find number of zeros in following expressions12 * 15 * 5 * 24 * 13 * 17 The Question can be easily solved if you can find the number of (2 * 5) combination in the expression Step 1Reformulating the expression into simpler form Step 2Number of 2 in above expression = 5Number …

## Questions: Number of Divisors

Question 01 Find the number of divisors of 1728Step 1: Factor Representation Step 2: Multiply Each Factor’s (Power+1)That is: ==> (6+1)*(3+1)==> 7 * 4==> 28 Hence there are 28 factors in 1728

## Concept: Number of Factors of number

Let us suppose you have given number 240 to find the number of factors Factor representation of 240 is Using conventional method, you can find number of factors by manual calculation So using this old method we can figure out that there are total 20 factors of number 240.But this method is tedious and consumes …

## Concept: Sum of Factors of number

Sum of Factors CalculationLet us suppose that you are asked to find the sum of all the factors of a number. Let the number be 240Factor representation of 240 will be like From the above representation, we can write total factors as You can see from the above calculations, there are 20 numbers which divide …

## Concept: Factors and its calculations

What are Factors of a number?Factors of any numbers are basically the digits which will fully divide that particular numberFor Example: 1. Factor of 6 are: 6=> 2*3 Here 2 and 3 are the digits which will fully divide number 6 Hence, 2 & 3 are factor of number 6 2. Calculate Individual factors of …