Factors of 138
2026-02-28 23:26 Diff
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Last updated on December 11, 2025

Factors are the numbers that divide any given number evenly without a 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 138, how they are used in real life, and tips to learn them quickly.

What are the Factors of 138?

The numbers that divide 138 evenly are known as factors of 138. A factor of 138 is a number that divides the number without a remainder. The factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.

Negative factors of 138: -1, -2, -3, -6, -23, -46, -69, and -138.

Prime factors of 138: 2, 3, and 23.

Prime factorization of 138: 2 × 3 × 23.

The sum of factors of 138: 1 + 2 + 3 + 6 + 23 + 46 + 69 + 138 = 288

How to Find Factors of 138?

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

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 138. Identifying the numbers which are multiplied to get the number 138 is the multiplication method.

Step 1: Multiply 138 by 1, 138 × 1 = 138.

Step 2: Check for other numbers that give 138 after multiplying     

2 × 69 = 138     

3 × 46 = 138    

 6 × 23 = 138

Therefore, the positive factor pairs of 138 are: (1, 138), (2, 69), (3, 46), and (6, 23). 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 a simple division method -

Step 1: Divide 138 by 1, 138 ÷ 1 = 138.

Step 2: Continue dividing 138 by the numbers until the remainder becomes 0.

138 ÷ 1 = 138

138 ÷ 2 = 69

138 ÷ 3 = 46

138 ÷ 6 = 23

Therefore, the factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138.

Prime Factors and Prime Factorization

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

Using Prime Factorization: In this process, prime factors of 138 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

138 ÷ 2 = 69

69 ÷ 3 = 23

23 ÷ 23 = 1

The prime factors of 138 are 2, 3, and 23. The prime factorization of 138 is: 2 × 3 × 23.

Factor Tree

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

Step 1: Firstly, 138 is divided by 2 to get 69.

Step 2: Now divide 69 by 3 to get 23.

Step 3: 23 is a prime number and cannot be divided further. So, the prime factorization of 138 is: 2 × 3 × 23.

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 138: (1, 138), (2, 69), (3, 46), and (6, 23).
  • Negative factor pairs of 138: (-1, -138), (-2, -69), (-3, -46), and (-6, -23).

Common Mistakes and How to Avoid Them in Factors of 138

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

A classroom has 138 desks and 6 rows. How many desks are in each row?

Okay, lets begin

There are 23 desks in each row.

Explanation

To divide the desks equally, we need to divide the total desks by the number of rows. 138/6 = 23

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Problem 2

A garden is rectangular, the length of the garden is 3 meters and the total area is 138 square meters. Find the width.

Okay, lets begin

46 meters.

Explanation

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

 Area = length × width     

138 = 3 × width     

To find the value of width, we need to shift 3 to the left side.     

138/3 = width     

Width = 46.

Well explained 👍

Problem 3

A school has 2 sections and 138 students. How many students will be in each section?

Okay, lets begin

Each section will have 69 students.

Explanation

To find the students in each section, divide the total students by the number of sections.     

138/2 = 69

Well explained 👍

Problem 4

A party has 138 guests and 23 tables. How many guests will sit at each table?

Okay, lets begin

There will be 6 guests at each table.

Explanation

Dividing the guests by the total tables, we will get the number of guests at each table.     

138/23 = 6

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Problem 5

138 apples need to be packed into 3 bags. How many apples will go in each bag?

Okay, lets begin

Each bag will have 46 apples.

Explanation

Divide total apples by the number of bags.     

138/3 = 46

Well explained 👍

FAQs on Factors of 138

1.What are the factors of 138?

1, 2, 3, 6, 23, 46, 69, 138 are the factors of 138.

2.Mention the prime factors of 138.

The prime factors of 138 are 2 × 3 × 23.

3.Is 138 a multiple of 6?

4.Mention the factor pairs of 138?

(1, 138), (2, 69), (3, 46), and (6, 23) are the factor pairs of 138.

5.What is the square of 138?

Important Glossaries for Factors of 138

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 23 are prime factors of 138.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are factor pairs. For example, the factor pairs of 138 are (1, 138), (2, 69), etc.
  • Prime factorization: The process of expressing a number as a product of its prime factors. For instance, the prime factorization of 138 is 2 × 3 × 23.
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method, we find that 6 × 23 = 138.

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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.