BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon102 Learners

Last updated on July 4th, 2025

Math Whiteboard Illustration

Divisor

Professor Greenline Explaining Math Concepts

A divisor is a number that divides another number, either completely or with a remainder. In math, division is used to split a number into equal parts, and the divisor plays a key role in this process. In this lesson, we will learn more about divisors.

Divisor for Australian Students
Professor Greenline from BrightChamps

What are Divisors?

A divisor is a number that divides another number, called the dividend. For example, if A divides B (i.e., B ÷ A), then A is a divisor of B, and A must be a nonzero number. In the division process, dividend, divisor, quotient, and remainder are the four most important terms. The quotient is the result of the division, and the remainder is the part left over when the dividend is not divisible evenly.

 

Take a look at this example: 30 ÷ 5

Dividend = 30

Divisor = 5

Quotient = 6

Remainder = 0

Professor Greenline from BrightChamps

Difference Between Divisors and Factors

In mathematics, divisors and factors both divide a number, but they differ in definition and context. However, they have some differences, which are listed below: 
 

Characteristics Divisors  Factors 
Definition It is a number that divides another number (dividend). Factors are numbers (positive or negative) that divide a number evenly without a remainder.
Remainder The remainder can be either zero or non-zero. The factor divides a number exactly, leaving no remainder.
Example 10 ÷ 3 = 3, with remainder 1 Factors of 50 - 1, 2, 5, 10, 25, 50.

 

Professor Greenline from BrightChamps

How to Find a Divisor?

To find the divisors of a number, we can follow a few methods. They are: 

 

Brute force method: In this method, all the numbers that divide the given number evenly are listed. These are the divisors, starting from 1 and including the number itself. For instance, the divisors of 10 are 1, 2, 5, and 10. 

 

Divisor using prime factorization: In this method, we need to split the given number into its prime factors. It is a method of showing a number as a product of its prime factors. For example, 10 can be written as:

10 = 2 × 5

Hence, the prime factorization of 10 is 2 × 5

 

The divisor can be found using different formulas based on two different cases. If the remainder is 0, the formula is: 

Divisor = Dividend ÷ Quotient 

If the remainder is non-zero, then the formula is: 

Divisor = (Dividend - Remainder) ÷ Quotient

Professor Greenline from BrightChamps

Properties of Divisors

Divisors are numbers that divide another number. This can result in a quotient with or without a remainder. The main properties of divisors are listed: 

 

  • A divisor cannot be zero (0) because dividing any number by zero is undefined. For example, 5 ÷ 0 = undefined.

 

  • If the divisor is 1, the quotient is always equal to the dividend. For example, 165 ÷ 1 = 165.

 

  • A number (dividend) can be divisible by both positive and negative divisors. For instance, (45 ÷ 9 =5 and 45 ÷ -9 = -5).

 

  • If both the dividend and divisor are the same, then the quotient will be 1. For example, 15 ÷ 15 = 1. 

 

  • When the dividend is an even number, it has at least one even divisor. For instance, the divisors of 10 include 1, 2, 5, and 10. 

 

  • If the divisor is a decimal, convert it into a whole number before performing the division.
Professor Greenline from BrightChamps

Real-Life Applications of Divisor

Divisors are useful in dividing quantities or resources into equal parts in real-life situations. Here are some real-world applications of divisors: 

 

  • We can use divisors to divide resources or objects among groups of people effectively. For instance, if we want to distribute 50 candies among 10 students, the divisor 10 helps to determine that each student gets 5 candies.

 

  • In manufacturing and production, divisors help to determine the total number of products packed in a box or the total number of containers loaded onto a truck.  

 

  • Engineers use divisors to calculate correct measurements when designing roads, buildings, or furniture. For example, if an engineer is constructing a 120 sq ft room and wants to divide it into 4 equal sections, they can use the divisor 4 to calculate the square footage of each section.

 

  • Divisors play a crucial role in economics, finance, and budgeting by aiding in the calculation of wages, expenses, and income. For example, if the government needs to distribute $15,000 among 10 citizens, the divisor 10 helps determine how much each person will receive.
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them on Divisor

Understanding the basics of division is useful for real-life calculations and problem-solving. However, students often make mistakes when working with divisors. Here are some common errors and tips to avoid them.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Thinking a Divisor and a Quotient are the Same

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students should remember that a divisor is the value used to divide the dividend, while the quotient is the result obtained from the division process. Sometimes, they mistakenly assume that the divisor is the same as the quotient.

 

For example, if we divide 65 ÷ 5 = 13
The dividend is 65, the divisor is 5, and the quotient is 13.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Incorrect Use of Formula

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

When applying the formulas for finding the divisors, students should be careful to use the correct one. If the remainder is zero, the formula for finding the divisor is:

Divisor = Dividend ÷ Quotient 

If the remainder is non-zero, the formula is: 

Divisor = (Dividend - Remainder) ÷ Quotient

If they apply the wrong formula, they will end up with incorrect results.

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Assuming Divisors are Smaller than the Dividend

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students should keep in mind that a divisor can be bigger than the given dividend. Sometimes, students mistakenly assume that a large number cannot be a divisor of a smaller number, leading them to wrong conclusions. If the divisor is larger than the dividend, the quotient will be less than 1. 

 

For instance, 6 ÷ 8 = 0.75

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Thinking a Divisor is Always a Whole Number.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Sometimes, students believe that divisors are always whole numbers. So, keep in mind that a divisor can be a decimal or a fraction; there is no rule stating that a divisor must always be a whole number.

 

For example, 100 ÷ 2.5 = 40. 

Mistake 5

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Believing Zero Can Be a Divisor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Remember, a divisor cannot be zero (0). If any number is divided by zero, the answer is undefined.

 

For example, (3 ÷ 0 = undefined). So, when we divide a number by zero, there is no answer to define.

arrow-right
Max from BrightChamps Saying "Hey"

Solved Examples of Divisor

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

What is the divisor if the dividend is 924, the quotient is 11, and the remainder is 0?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

84

Explanation

If the remainder is 0, we can use the formula:

Divisor = Dividend ÷ Quotient 

Divisor = 924 ÷  11 = 84

The divisor is 84.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

What is the divisor if the dividend is 187, the quotient is 20, and the remainder is 7?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

9

Explanation

If the remainder is a non-zero number, then the formula is: 

Divisor = (Dividend - Remainder) ÷ Quotient 

Now, substitute the values: 

Divisor = (187 - 7) ÷ 20 

= 180 ÷ 20 = 9

The divisor is 9.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

What is the divisor if the dividend is 225, the quotient is 15, and the remainder is 0?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

15

Explanation

If the remainder is 0, we can use the formula:

Divisor = Dividend ÷ Quotient 

Divisor = 225 ÷ 15 = 15

The divisor is 15.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Check if 7 is a divisor of 56.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 7 is a divisor of 56.

Explanation

To know whether 7 is a divisor of 56, we must divide 56 by 7.
56 ÷ 7 = 8 

The quotient is 8, which is a whole number, and the remainder is 0.

Therefore, 7 is a divisor of 56.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

What is the divisor if the dividend is 144, the quotient is 12, and the remainder is 0?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

12

Explanation

If the remainder is 0, we can use the formula:

Divisor = Dividend ÷ Quotient 

Divisor = 144  ÷ 12 = 12 

The divisor is 12.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Divisor

1.Define a divisor.

Math FAQ Answers Dropdown Arrow

2.Can a divisor be zero?

Math FAQ Answers Dropdown Arrow

3.What are the formulas for finding a divisor?

Math FAQ Answers Dropdown Arrow

4.Can a divisor always be a whole number?

Math FAQ Answers Dropdown Arrow

5.How can children in Australia use numbers in everyday life to understand Divisor?

Math FAQ Answers Dropdown Arrow

6.What are some fun ways kids in Australia can practice Divisor with numbers?

Math FAQ Answers Dropdown Arrow

7.What role do numbers and Divisor play in helping children in Australia develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

8.How can families in Australia create number-rich environments to improve Divisor skills?

Math FAQ Answers Dropdown Arrow
Math Teacher Background Image
Math Teacher Image

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom