Factors of 238
2026-02-28 12:53 Diff
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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 238, how they are used in real life, and tips to learn them quickly.

What are the Factors of 238?

The numbers that divide 238 evenly are known as factors of 238.

A factor of 238 is a number that divides the number without a remainder.
 

The factors of 238 are 1, 2, 7, 14, 17, 34, 119, and 238.

Negative factors of 238: -1, -2, -7, -14, -17, -34, -119, and -238.

Prime factors of 238: 2 and 17.

Prime factorization of 238: 2 × 119 = 2 × 7 × 17.

The sum of factors of 238: 1 + 2 + 7 + 14 + 17 + 34 + 119 + 238 = 432

How to Find Factors of 238?

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 238. Identifying the numbers that are multiplied to get the number 238 is the multiplication method.

Step 1: Multiply 238 by 1, 238 × 1 = 238.

Step 2: Check for other numbers that give 238 after multiplying 2 × 119 = 238 7 × 34 = 238 14 × 17 = 238

Therefore, the positive factor pairs of 238 are: (1, 238), (2, 119), (7, 34), (14, 17). 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 a simple division method -

Step 1: Divide 238 by 1, 238 ÷ 1 = 238.

Step 2: Continue dividing 238 by the numbers until the remainder becomes 0.

238 ÷ 1 = 238

238 ÷ 2 = 119

238 ÷ 7 = 34

238 ÷ 14 = 17

Therefore, the factors of 238 are: 1, 2, 7, 14, 17, 34, 119, 238.

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

238 ÷ 2 = 119

119 ÷ 7 = 17

17 ÷ 17 = 1

The prime factors of 238 are 2 and 17.

The prime factorization of 238 is: 2 × 7 × 17.

Factor Tree

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

Step 1: Firstly, 238 is divided by 2 to get 119.

Step 2: Now divide 119 by 7 to get 17.

Step 3: 17 is a prime number and cannot be divided further.

So, the prime factorization of 238 is: 2 × 7 × 17.

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 238: (1, 238), (2, 119), (7, 34), (14, 17).

Negative factor pairs of 238: (-1, -238), (-2, -119), (-7, -34), (-14, -17).

Common Mistakes and How to Avoid Them in Factors of 238

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

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Problem 1

There are 14 students and 238 pencils. How will they divide them equally?

Okay, lets begin

They will get 17 pencils each.

Explanation

To divide the pencils equally, we need to divide the total pencils by the number of students.

238/14 = 17

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 17 meters and the total area is 238 square meters. Find the width?

Okay, lets begin

14 meters.

Explanation

To find the width of the garden, we use the formula, Area = length × width

238 = 17 × width

To find the value of width, we need to shift 17 to the left side.

238/17 = width

Width = 14.

Well explained 👍

Problem 3

There are 119 apples and 238 baskets. How many apples will be in each basket?

Okay, lets begin

Each basket will have 2 apples.

Explanation

To find the apples in each basket, divide the total apples by the baskets.

238/119 = 2

Well explained 👍

Problem 4

In a class, there are 238 students, and 7 groups. How many students are there in each group?

Okay, lets begin

There are 34 students in each group.

Explanation

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

238/7 = 34

Well explained 👍

Problem 5

238 books need to be arranged in 17 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 14 books.

Explanation

Divide total books by shelves.

238/17 = 14

Well explained 👍

FAQs on Factors of 238

1.What are the factors of 238?

1, 2, 7, 14, 17, 34, 119, 238 are the factors of 238.

2.Mention the prime factors of 238.

The prime factors of 238 are 2 × 7 × 17.

3.Is 238 a multiple of 7?

4.Mention the factor pairs of 238?

(1, 238), (2, 119), (7, 34), (14, 17) are the factor pairs of 238.

5.What is the square of 238?

Important Glossaries for Factor of 238

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 238 are 1, 2, 7, 14, 17, 34, 119, and 238.
  • Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of 238.
  • 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 238 are (1, 238), (2, 119), etc.
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 238 is 2 × 7 × 17.
  • Divisibility: The ability of one number to be divided by another without leaving a remainder. For example, 238 is divisible by 2, 7, and 17.

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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.