102 LearnersLast updated on May 26th, 2025
Factors of 238
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.
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
- Using factor tree
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.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself
For example, in factors of 238, 1 and 238 are also factors.
Factors of 238 Examples
Problem 1
There are 14 students and 238 pencils. How will they divide them equally?
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
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?
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.
Problem 3
There are 119 apples and 238 baskets. How many apples will be in each basket?
Each basket will have 2 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
238/119 = 2
Problem 4
In a class, there are 238 students, and 7 groups. How many students are there in each group?
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
Problem 5
238 books need to be arranged in 17 shelves. How many books will go on each shelf?
Each of the shelves has 14 books.
Explanation
Divide total books by shelves.
238/17 = 14
FAQs on Factors of 238
1.What are the factors of 238?
2.Mention the prime factors of 238.
3.Is 238 a multiple of 7?
4.Mention the factor pairs of 238?
5.What is the square of 238?
6.How can children in United States use numbers in everyday life to understand Factors of 238?
7.What are some fun ways kids in United States can practice Factors of 238 with numbers?
8.What role do numbers and Factors of 238 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 238 skills?
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
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