Factors of 981
2026-02-28 17:35 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 981, how they are used in real life, and tips to learn them quickly.

What are the Factors of 981?

The numbers that divide 981 evenly are known as factors of 981.

A factor of 981 is a number that divides the number without a remainder.

The factors of 981 are 1, 3, 9, 109, 327, and 981.

Negative factors of 981: -1, -3, -9, -109, -327, and -981.

Prime factors of 981: 3 and 109.

Prime factorization of 981: 3² × 109.

The sum of factors of 981: 1 + 3 + 9 + 109 + 327 + 981 = 1430

How to Find Factors of 981?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 981. Identifying the numbers which are multiplied to get the number 981 is the multiplication method.

Step 1: Multiply 981 by 1, 981 × 1 = 981.

Step 2: Check for other numbers that give 981 after multiplying 3 × 327 = 981 9 × 109 = 981

Therefore, the positive factor pairs of 981 are: (1, 981), (3, 327), (9, 109).

All these factor pairs result in 981.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method

Step 1: Divide 981 by 1, 981 ÷ 1 = 981.

Step 2: Continue dividing 981 by the numbers until the remainder becomes 0.

981 ÷ 1 = 981

981 ÷ 3 = 327

981 ÷ 9 = 109

Therefore, the factors of 981 are: 1, 3, 9, 109, 327, 981.

Prime Factors and Prime Factorization

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 981 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

981 ÷ 3 = 327

327 ÷ 3 = 109

109 ÷ 109 = 1

The prime factors of 981 are 3 and 109.

The prime factorization of 981 is: 3² × 109.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 981 is divided by 3 to get 327.

Step 2: Now divide 327 by 3 to get 109.

Step 3: Here, 109 is a prime number, that cannot be divided anymore. So, the prime factorization of 981 is: 3² × 109.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 981: (1, 981), (3, 327), (9, 109).

Negative factor pairs of 981: (-1, -981), (-3, -327), (-9, -109).

Common Mistakes and How to Avoid Them in Factors of 981

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

A team of 9 people has 981 candies. How will they divide it equally?

Okay, lets begin

They will get 109 candies each.

Explanation

To divide the candies equally, we need to divide the total candies by the number of people.

981/9 = 109

Well explained 👍

Problem 2

A rectangular hall has a length of 3 meters and a total area of 981 square meters. Find its width.

Okay, lets begin

327 meters.

Explanation

To find the width of the hall, we use the formula

Area = length × width

981 = 3 × width

To find the value of width, we need to shift 3 to the left side.

981/3 = width

Width = 327.

Well explained 👍

Problem 3

There are 3 sections in a library with a total of 981 books. How many books are in each section?

Okay, lets begin

Each section will have 327 books.

Explanation

To find the books in each section, divide the total books by the number of sections.

981/3 = 327

Well explained 👍

Problem 4

In a competition, there are 327 participants and 3 teams. How many participants are in each team?

Okay, lets begin

There are 109 participants in each team.

Explanation

Dividing the participants by the total teams, we will get the number of participants in each team.

327/3 = 109

Well explained 👍

Problem 5

981 trees need to be planted in 9 rows. How many trees will go in each row?

Okay, lets begin

Each row will have 109 trees.

Explanation

Divide total trees by the number of rows.

981/9 = 109

Well explained 👍

FAQs on Factors of 981

1.What are the factors of 981?

1, 3, 9, 109, 327, 981 are the factors of 981.

2.Mention the prime factors of 981.

The prime factors of 981 are 3² × 109.

3.Is 981 a multiple of 9?

4.Mention the factor pairs of 981?

(1, 981), (3, 327), (9, 109) are the factor pairs of 981.

5.What is the square of 981?

Important Glossaries for Factor of 981

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 981 are 1, 3, 9, 109, 327, and 981.
     
  • Prime factors: The factors which are prime numbers. For example, 3 and 109 are prime factors of 981.
     
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 981 are (1, 981), (3, 327), etc.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, 981 is expressed as 3² × 109.
     
  • Divisibility: The ability of one number to be divided by another without a remainder. For example, 9 is a factor of 981 because 981 can be divided by 9 without a remainder.

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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.

Fun Fact

: She loves to read number jokes and games.