101 LearnersLast updated on May 26th, 2025
Factors of 1089
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.
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
- Using factor tree
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.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1089, 1 and 1089 is also a factor.
Factors of 1089 Examples
Problem 1
There are 9 students and 1089 pencils. How will they divide it equally?
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
Problem 2
A square garden has an area of 1089 square meters. What is the length of each side?
33 meters.
Explanation
To find the side of the square garden, we use the formula,
Area = side × side
√1089 = side
Side = 33.
Problem 3
There are 33 chairs and 1089 people. How many people will be seated on each chair?
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
Problem 4
In a conference, there are 1089 attendees and 11 rooms. How many attendees are there in each room?
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
Problem 5
1089 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has 99 books.
Explanation
Divide total books with shelves.
1089 ÷ 11 = 99
FAQs on Factors of 1089
1.What are the factors of 1089?
2.Mention the prime factors of 1089.
3.Is 1089, a multiple of 9?
4.Mention the factor pairs of 1089?
5.What is the square of 1089?
6.How can children in Australia use numbers in everyday life to understand Factors of 1089?
7.What are some fun ways kids in Australia can practice Factors of 1089 with numbers?
8.What role do numbers and Factors of 1089 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 1089 skills?
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
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