Factors of 1053
2026-02-28 11:51 Diff

210 Learners

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 1053, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 1053?

The numbers that divide 1053 evenly are known as factors of 1053.

A factor of 1053 is a number that divides the number without remainder.

The factors of 1053 are 1, 3, 9, 117, 351, and 1053.

Negative factors of 1053: -1, -3, -9, -117, -351, and -1053.

Prime factors of 1053: 3 and 117.

Prime factorization of 1053: 3 × 3 × 117.

The sum of factors of 1053: 1 + 3 + 9 + 117 + 351 + 1053 = 1534

How to Find Factors of 1053?

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 1053. Identifying the numbers which are multiplied to get the number 1053 is the multiplication method.

Step 1: Multiply 1053 by 1, 1053 × 1 = 1053.

Step 2: Check for other numbers that give 1053 after multiplying

3 × 351 = 1053

9 × 117 = 1053

Therefore, the positive factor pairs of 1053 are: (1, 1053), (3, 351), (9, 117). All these factor pairs result in 1053. 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 simple division method -

Step 1: Divide 1053 by 1, 1053 ÷ 1 = 1053.

Step 2: Continue dividing 1053 by the numbers until the remainder becomes

1053 ÷ 1 = 1053

1053 ÷ 3 = 351

1053 ÷ 9 = 117

Therefore, the factors of 1053 are: 1, 3, 9, 117, 351, and 1053.

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 1053 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1053 ÷ 3 = 351

351 ÷ 3 = 117

117 ÷ 3 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of 1053 are 3 and 13

 The prime factorization of 1053 is: 3 × 3 × 3 × 13.

Factor Tree

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

Step 1: Firstly, 1053 is divided by 3 to get 351.

Step 2: Now divide 351 by 3 to get 117.

Step 3: Then divide 117 by 3 to get 39.

Step 4: Divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1053 is: 3 × 3 × 3 × 13.

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 1053: (1, 1053), (3, 351), (9, 117).

Negative factor pairs of 1053: (-1, -1053), (-3, -351), (-9, -117).

Common Mistakes and How to Avoid Them in Factors of 1053

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 3 friends and 1053 candies. How will they divide it equally?

Okay, lets begin

They will get 351 candies each.

Explanation

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

1053/3 = 351

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 9 meters and the total area is 1053 square meters. Find the width.

Okay, lets begin

117 meters.

Explanation

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

Area = length × width

1053 = 9 × width

To find the value of width, we need to shift 9 to the left side.

1053/9 = width

Width = 117.

Well explained 👍

Problem 3

There are 117 bags and 1053 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 9 candies.

Explanation

To find the candies in each bag, divide the total candies by the number of bags.

1053/117 = 9

Well explained 👍

Problem 4

In a class, there are 1053 students, and 9 groups. How many students are there in each group?

Okay, lets begin

There are 117 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.

1053/9 = 117

Well explained 👍

Problem 5

1053 books need to be arranged in 3 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 351 books.

Explanation

Divide total books by the number of shelves.

1053/3 = 351

Well explained 👍

FAQs on Factors of 1053

1.What are the factors of 1053?

1, 3, 9, 117, 351, and 1053 are the factors of 1053.

2.Mention the prime factors of 1053.

The prime factors of 1053 are 3 and 13.

3.Is 1053 a multiple of 9?

4.Mention the factor pairs of 1053?

(1, 1053), (3, 351), (9, 117) are the factor pairs of 1053.

5.What is the square of 1053?

The square of 1053 is 1108809.

Important Glossaries for Factors of 1053

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1053 are 1, 3, 9, 117, 351, and 1053.
  • Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 1053.
  • 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 1053 are (1, 1053), (3, 351), and (9, 117).
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1053 is 3 × 3 × 3 × 13.
  • Multiplication method: A method for finding factors where pairs of numbers are multiplied to give the original number, such as finding factor pairs of 1053.

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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.