# Divisor

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 1 Introduction to Divisor 2 What is a Divisor? 3 Difference between Factors & Divisors 4 How to find a Divisor? 5 Important Notes on Divisor 8 Solved Examples on Divisor 9 Thinking out of the Box! 10 Practice Questions on Divisor 11 Maths Olympiad Sample Papers 12 Frequently Asked Questions (FAQs)

## Introduction to Divisor

Division means dividing something in equal parts or groups.

You probably use division in your day to day life and don't even realize it.

For example, let's assume that it is your birthday and you want to distribute a packet of candies among your friends in school.

You want to share the candies equally among your friends.

How will you know the number of candies each one will get?

To find the answer, you must divide the number of candies by the number of friends.

If there are 32 candies in your packet and you have 8 friends, the mathematical equation for division will be:

$$\bf{32\div8=4}$$

Each of your friends will get 4 candies.

Numbers used in division have certain names that describe them.

All 3 numbers have unique names.

In this equation, the number 32 is the dividend, 8 is the divisor and 4 is the quotient.

## What is a Divisor?

### Divisor: Definition in Math

The number we are dividing by is called a divisor.

Divisor takes the dividend and divides it in to smaller parts.

### Divisor and Dividend

The number being divided in a division problem is called a dividend and the number that the dividend divides is called the divisor.

Input the divisor and dividend in the simulation given below by moving the points on the two bars.

You will be able to find out how the divisor divides the dividend.

### Ways to write a division problem

There are 3 different ways to write a division problem.

Don't get confused! All these mean the same thing.

You've already seen one way of writing it.

Let's have a quick look at the other two ways.

The division problem shown below is exactly the same as the one shown above.

The third way to write the division problem is given below.

Again, this is the same as the division problem shown above.

## Difference between Factors and Divisors

Divisor is any number that divides the other number whereas a factor is a number that divides the other number and leaves the remainder 0

Thus, all factors are divisors but all divisors are not factors.

The following image shows the factor tree of a number 24

Thus, the only factors of 24 are 2 and 3

Let us divide 24 by 5

Since 5 does not give the remainder 0, it is not a factor of 24

## How to find a Divisor?

Let us recall the different terms of division.

The number 35 is the dividend. It is the number to be divided.

The number 5 is the divisor. It is the number that divides the dividend.

The number 7 is the quotient. It is the answer we get after dividing.

The number 0 is the remainder. It is the number which is left over after dividing.

### Divisor: Formula

Remember that if the remainder is 0, then

 $$\text{Divisor}=\text{Dividend}\div\text{Quotient}$$

Important Notes
1. You can never divide a number by 0
2. A division problem stays true even if we swap quotient and divisor
3. 0 divided by any divisor gives 0 as the quotient
4. A number divided by 1 gives the number itself as the quotient
5. When the dividend and the divisor are equal in a division problem, the answer to such a problem is always 1
6. The remainder is always smaller than or equal to the divisor

## Divisor: Examples

 Example 1

The children in a school are happy because they are celebrating Children's Day.

Each child will get 3 colour boxes from the school.

The school has 279 colour boxes.

The children are curious to know how many of them will get them.

Can you find out?

Solution:

Number of colour boxes = 279

Number of colour boxes each child will get = 3

Number of children who will get 3 colour boxes

$$= 279\div3$$

Dividing 279 by 3, we get the quotient as 93

 $$\therefore$$ 93 children will get colour boxes.
 Example 2

A gardener bought 325 trees.

He wants to plant 13 trees in each row.

However, he doesn't know the number of rows he will need to plant the trees.

Can you find the number of rows he will need?

Solution:

Number of trees = 325

Number of trees in each row = 13

Number of rows required to plant 13 trees

$$=325\div13$$

Dividing 325 by 13, we get the quotient as 25

 $$\therefore$$ He needs 25 rows to plant the trees.
 Example 3

Edwin took a loan of Rs. 63,000 from a bank to pay his fees for coaching classes.

He will pay the loan to the bank each month in equal installments for 6 months.

How much will he pay each month to the bank?

Solution:

Divide Rs. 63,000 for 6 months to find the amount Edwin will pay to the bank each month.

Hence, the amount paid by Edwin each month

= $$63,000\div6$$

 $$\therefore$$ Edwin pays Rs. 10,500 each month.
 Example 4

A school decided to take their students for a summer camp during their summer holidays. 352 children will be going on the trip.

22 tents are available for the camp.

Can you calculate the number of children that can be accommodated in each tent?

Solution:

To find the number of children in each tent, we will divide the number of tents among the total number of children.

So, the number of children each tent has

= $$352\div 22$$

 $$\therefore$$ 16 children can be accommodated in each tent.

Think Tank
 1. Emma bought a battery which mentioned “Life: 4000 hours” on its label. She uses the battery throughout the day. How many days will the battery last?

## Practice Questions

Here are few activities for you to practice.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is a divisor?

Divisor: Definition in Math - A number that divides another number is called a divisor.

If we divide 42 by 7, we get 6

Here, 7 divides 42 in to 6 equal parts.

In this example, 7 is a divisor.

## 2. Is a number a divisor of itself?

Yes, a number is a divisor of itself because a number can divide itself in only 1 part.

This means that it will give the quotient as 1

## 3. What is the divisor in a fraction?

A fraction is represented in the form \begin{align}\frac{p}{q}\end{align}, $$q\neq0$$. Here, the denominator \begin{align}q\end{align} is the divisor.

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