Factors of 1107
2026-02-28 23:46 Diff
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Last updated on December 15, 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 1107, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1107?

The numbers that divide 1107 evenly are known as factors of 1107.

A factor of 1107 is a number that divides the number without a remainder.

The factors of 1107 are 1, 3, 369, and 1107.

Negative factors of 1107: -1, -3, -369, and -1107.

Prime factors of 1107: 3, 7, and 53.

Prime factorization of 1107: 3 × 7 × 53.

The sum of factors of 1107: 1 + 3 + 369 + 1107 = 1480

How to Find Factors of 1107?

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

  • Finding factors using multiplication
  • Finding factors using the 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 1107. Identifying the numbers that are multiplied to get the number 1107 is the multiplication method.

Step 1: Multiply 1107 by 1, 1107 × 1 = 1107.

Step 2: Check for other numbers that give 1107 after multiplying 3 × 369 = 1107

Therefore, the positive factor pairs of 1107 are: (1, 1107) and (3, 369).

All these factor pairs result in 1107.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the 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 1107 by 1, 1107 ÷ 1 = 1107.

Step 2: Continue dividing 1107 by the numbers until the remainder becomes 0.

1107 ÷ 1 = 1107

1107 ÷ 3 = 369

Therefore, the factors of 1107 are: 1, 3, 369, 1107.

Prime Factors and Prime Factorization

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

Using Prime Factorization: In this process, prime factors of 1107 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1107 ÷ 3 = 369

369 ÷ 3 = 123

123 ÷ 3 = 41

41 ÷ 41 = 1

The prime factors of 1107 are 3, 7, and 53.

The prime factorization of 1107 is: 3 × 7 × 53.

Factor Tree

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

Step 1: Firstly, 1107 is divided by 3 to get 369.

Step 2: Now divide 369 by 3 to get 123.

Step 3: Then divide 123 by 3 to get 41.

Step 4: Divide 41 by 41 to get 1. Here, 41 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 1107 is: 3 × 7 × 53.

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 1107: (1, 1107) and (3, 369).

Negative factor pairs of 1107: (-1, -1107) and (-3, -369).

Common Mistakes and How to Avoid Them in Factors of 1107

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 teams and 1107 participants. How will the teams be divided equally?

Okay, lets begin

Each team will have 369 participants.

Explanation

To divide the participants equally, we need to divide the total participants by the number of teams.

1107/3 = 369

Well explained 👍

Problem 2

A rectangular plot has a length of 369 meters and a total area of 1107 square meters. Find the width.

Okay, lets begin

3 meters.

Explanation

To find the width of the plot, we use the formula, Area = length × width 1107 = 369 × width

To find the value of width, we need to shift 369 to the left side.

1107/369 = width

Width = 3.

Well explained 👍

Problem 3

There are 7 conferences and 1107 attendees. How many attendees will be in each conference?

Okay, lets begin

Each conference will have 158 attendees.

Explanation

To find the attendees in each conference, divide the total attendees by the conferences.

1107/7 = 158

Well explained 👍

Problem 4

In a school, there are 1107 students, and 41 classes. How many students are there in each class?

Okay, lets begin

There are 27 students in each class.

Explanation

Dividing the students by the total classes, we will get the number of students in each class.

1107/41 = 27

Well explained 👍

Problem 5

1107 books need to be arranged in 369 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 3 books.

Explanation

Divide total books by shelves.

1107/369 = 3

Well explained 👍

FAQs on Factors of 1107

1.What are the factors of 1107?

1, 3, 369, and 1107 are the factors of 1107.

2.Mention the prime factors of 1107.

The prime factors of 1107 are 3, 7, and 53.

3.Is 1107 a multiple of 3?

4.Mention the factor pairs of 1107?

(1, 1107) and (3, 369) are the factor pairs of 1107.

5.What is the square of 1107?

The square of 1107 is 1225449.

Important Glossaries for Factors of 1107

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1107 are 1, 3, 369, and 1107.
  • Prime factors: The factors which are prime numbers. For example, 3, 7, and 53 are prime factors of 1107.
  • 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 1107 are (1, 1107) and (3, 369).
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1107 is 3 × 7 × 53.
  • Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the target number, such as finding that 3 and 369 multiply to 1107.

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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.