Factors of 117
2026-02-28 10:00 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-117

327 Learners

Last updated on December 11, 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 117, how they are used in real life, and tips to learn them quickly.

What are the Factors of 117?

The numbers that divide 117 evenly are known as factors of 117. A factor of 117 is a number that divides the number without remainder. The factors of 117 are 1, 3, 9, 13, 39, and 117.

Negative factors of 117: -1, -3, -9, -13, -39, and -117.

Prime factors of 117: 3 and 13.

Prime factorization of 117: 3² × 13.

The sum of factors of 117: 1 + 3 + 9 + 13 + 39 + 117 = 182

How to Find Factors of 117?

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

  1. Finding factors using multiplication
  2. Finding factors using division method
  3. 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 117. Identifying the numbers which are multiplied to get the number 117 is the multiplication method.

Step 1: Multiply 117 by 1, 117 × 1 = 117.

Step 2: Check for other numbers that give 117 after multiplying 3 × 39 = 117 9 × 13 = 117

Therefore, the positive factor pairs of 117 are: (1, 117), (3, 39), (9, 13).

All these factor pairs result in 117. For every positive factor, there is a negative factor.

Explore Our Programs

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 a simple division method -

Step 1: Divide 117 by 1, 117 ÷ 1 = 117.

Step 2: Continue dividing 117 by the numbers until the remainder becomes 0.

117 ÷ 1 = 117

117 ÷ 3 = 39

117 ÷ 9 = 13

Therefore, the factors of 117 are: 1, 3, 9, 13, 39, 117.

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

117 ÷ 3 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of 117 are 3 and 13. The prime factorization of 117 is: 3² × 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, 117 is divided by 3 to get 39.

Step 2: Now divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 117 is: 3² × 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 117: (1, 117), (3, 39), (9, 13).
  • Negative factor pairs of 117: (-1, -117), (-3, -39), (-9, -13).

Common Mistakes and How to Avoid Them in Factors of 117

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

Download Worksheets

Problem 1

There are 13 students and 117 apples. How will they divide them equally?

Okay, lets begin

They will get 9 apples each.

Explanation

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

117/13 = 9

Well explained 👍

Problem 2

A plot is rectangular, and the length of the plot is 9 meters with a total area of 117 square meters. Find the width.

Okay, lets begin

13 meters.

Explanation

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

Area = length × width

117 = 9 × width

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

117/9 = width

Width = 13.

Well explained 👍

Problem 3

There are 39 gift bags and 117 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 3 candies.

Explanation

To find the candies in each bag, divide the total candies with the bags.

117/39 = 3

Well explained 👍

Problem 4

In a class, there are 117 students, and 3 sections. How many students are there in each section?

Okay, lets begin

There are 39 students in each section.

Explanation

Dividing the students with the total sections, we will get the number of students in each section.

117/3 = 39

Well explained 👍

Problem 5

117 books need to be distributed in 9 classrooms. How many books will go to each classroom?

Okay, lets begin

Each classroom will receive 13 books.

Explanation

Divide total books with classrooms.

117/9 = 13

Well explained 👍

FAQs on Factors of 117

1.What are the factors of 117?

1, 3, 9, 13, 39, 117 are the factors of 117.

2.Mention the prime factors of 117.

The prime factors of 117 are 3² × 13.

3.Is 117 a multiple of 9?

4.Mention the factor pairs of 117.

(1, 117), (3, 39), (9, 13) are the factor pairs of 117.

5.What is the square of 117?

Important Glossaries for Factors of 117

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 117 are 1, 3, 9, 13, 39, and 117.
  • Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 117.
  • 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 117 are (1, 117), (3, 39), etc.
  • Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the target number.
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, 117 = 3² × 13.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.