Factors of 1089
2026-02-28 10:16 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without 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 1089, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 1089?

The numbers that divide 1089 evenly are known as factors of 1089.

A factor of 1089 is a number that divides the number without remainder.

The factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089.

Negative factors of 1089: -1, -3, -9, -11, -33, -99, -121, -363, and -1089.

Prime factors of 1089: 3 and 11.

Prime factorization of 1089: 3² × 11².

The sum of factors of 1089: 1 + 3 + 9 + 11 + 33 + 99 + 121 + 363 + 1089 = 1729

How to Find Factors of 1089?

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

  • Finding factors using multiplication
     
  • Finding factors using division method
     
  • Prime factors and Prime factorization

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1089. Identifying the numbers which are multiplied to get the number 1089 is the multiplication method.

Step 1: Multiply 1089 by 1, 1089 × 1 = 1089.

Step 2: Check for other numbers that give 1089 after multiplying

3 × 363 = 1089

9 × 121 = 1089

11 × 99 = 1089

Therefore, the positive factor pairs of 1089 are: (1, 1089), (3, 363), (9, 121), (11, 99).

All these factor pairs result in 1089.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given number 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 a simple division method -

Step 1: Divide 1089 by 1, 1089 ÷ 1 = 1089.

Step 2: Continue dividing 1089 by the numbers until the remainder becomes 0.

1089 ÷ 1 = 1089

1089 ÷ 3 = 363

1089 ÷ 9 = 121

1089 ÷ 11 = 99

Therefore, the factors of 1089 are: 1, 3, 9, 11, 33, 99, 121, 363, 1089.

Prime Factors and Prime Factorization

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

Using Prime Factorization: In this process, prime factors of 1089 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

1089 ÷ 3 = 363

363 ÷ 3 = 121

121 ÷ 11 = 11

11 ÷ 11 = 1

The prime factors of 1089 are 3 and 11.

The prime factorization of 1089 is: 3² × 11².

Factor Tree

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

Step 1: Firstly, 1089 is divided by 3 to get 363.

Step 2: Now divide 363 by 3 to get 121.

Step 3: Then divide 121 by 11 to get 11.

Here, 11 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 1089 is: 3² × 11².

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 1089: (1, 1089), (3, 363), (9, 121), (11, 99).

Negative factor pairs of 1089: (-1, -1089), (-3, -363), (-9, -121), (-11, -99).

Common Mistakes and How to Avoid Them in Factors of 1089

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

There are 9 students and 1089 pencils. How will they divide it equally?

Okay, lets begin

They will get 121 pencils each.

Explanation

To divide the pencils equally, we need to divide the total pencils with the number of students.

1089 ÷ 9 = 121

Well explained 👍

Problem 2

A square garden has an area of 1089 square meters. What is the length of each side?

Okay, lets begin

33 meters.

Explanation

To find the side of the square garden, we use the formula,

Area = side × side

√1089 = side

Side = 33.

Well explained 👍

Problem 3

There are 33 chairs and 1089 people. How many people will be seated on each chair?

Okay, lets begin

Each chair will have 33 people.

Explanation

To find the number of people on each chair, divide the total people by the number of chairs.

1089 ÷ 33 = 33

Well explained 👍

Problem 4

In a conference, there are 1089 attendees and 11 rooms. How many attendees are there in each room?

Okay, lets begin

There are 99 attendees in each room.

Explanation

Dividing the attendees with the total rooms, we will get the number of attendees in each room.

1089 ÷ 11 = 99

Well explained 👍

Problem 5

1089 books need to be arranged in 11 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 99 books.

Explanation

Divide total books with shelves.

1089 ÷ 11 = 99

Well explained 👍

FAQs on Factors of 1089

1.What are the factors of 1089?

1, 3, 9, 11, 33, 99, 121, 363, 1089 are the factors of 1089.

2.Mention the prime factors of 1089.

The prime factors of 1089 are 3² × 11².

3.Is 1089, a multiple of 9?

4.Mention the factor pairs of 1089?

(1, 1089), (3, 363), (9, 121), (11, 99) are the factor pairs of 1089.

5.What is the square of 1089?

The square of 1089 is 1185921.

Important Glossaries for Factor of 1089

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089.
     
  • Prime factors: The factors which are prime numbers. For example, 3 and 11 are prime factors of 1089.
     
  • 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 1089 are (1, 1089), (3, 363), etc.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1089 is 3² × 11².
     
  • Multiplication method: A method used to find factors by identifying pairs of numbers multiplied to get the original number. For example, using the multiplication method to find factors of 1089.

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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.