127 LearnersLast updated on May 26th, 2025
Factors of 234
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 234, how they are used in real life, and tips to learn them quickly.
What are the Factors of 234?
The numbers that divide 234 evenly are known as factors of 234.
A factor of 234 is a number that divides the number without remainder.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234.
Negative factors of 234: -1, -2, -3, -6, -9, -13, -18, -26, -39, -78, -117, and -234.
Prime factors of 234: 2, 3, and 13.
Prime factorization of 234: 2 × 3² × 13.
The sum of factors of 234: 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 39 + 78 + 117 + 234 = 546.
How to Find Factors of 234?
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 234. Identifying the numbers which are multiplied to get the number 234 is the multiplication method.
Step 1: Multiply 234 by 1, 234 × 1 = 234.
Step 2: Check for other numbers that give 234 after multiplying
2 × 117 = 234
3 × 78 = 234
6 × 39 = 234
9 × 26 = 234
13 × 18 = 234
Therefore, the positive factor pairs of 234 are: (1, 234), (2, 117), (3, 78), (6, 39), (9, 26), (13, 18).
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 the simple division method -
Step 1: Divide 234 by 1, 234 ÷ 1 = 234.
Step 2: Continue dividing 234 by the numbers until the remainder becomes 0.
234 ÷ 1 = 234
234 ÷ 2 = 117
234 ÷ 3 = 78
234 ÷ 6 = 39
234 ÷ 9 = 26
234 ÷ 13 = 18
Therefore, the factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
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
- Using factor tree
Using Prime Factorization: In this process, prime factors of 234 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
234 ÷ 2 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 234 are 2, 3, and 13.
The prime factorization of 234 is: 2 × 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, 234 is divided by 2 to get 117.
Step 2: Now divide 117 by 3 to get 39.
Step 3: Then divide 39 by 3 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 234 is: 2 × 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 234: (1, 234), (2, 117), (3, 78), (6, 39), (9, 26), and (13, 18).
Negative factor pairs of 234: (-1, -234), (-2, -117), (-3, -78), (-6, -39), (-9, -26), and (-13, -18).
Common Mistakes and How to Avoid Them in Factors of 234
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the 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 word. Always remember to include 1 and the number itself.
For example, in factors of 234, 1 and 234 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 234 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 234/1.5 = 156, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 234 are prime numbers. For example, 2, 3, and 13 are the prime factors of 234, but it has other factors like 6, 18.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 234 as 2 × 3² × 13 and missing all the key factors.
Factors of 234 Examples
Problem 1
There are 13 teams and 234 trophies. How will they distribute them equally?
They will get 18 trophies each.
Explanation
To divide the trophies equally, we need to divide the total trophies with the number of teams.
234/13 = 18
Problem 2
A garden is rectangular, the length of the garden is 13 meters and the total area is 234 square meters. Find the width?
18 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
234 = 13 × width
To find the value of width, we need to shift 13 to the left side.
234/13 = width
Width = 18.
Problem 3
There are 6 gift boxes and 234 chocolates. How many chocolates will be in each box?
Each box will have 39 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates with the boxes.
234/6 = 39
Problem 4
In a conference, there are 234 participants, and 9 groups. How many participants are there in each group?
There are 26 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
234/9 = 26
Problem 5
234 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 78 books.
Explanation
Divide total books with shelves.
234/3 = 78
FAQs on Factors of 234
1.What are the factors of 234?
2.Mention the prime factors of 234.
3.Is 234 a multiple of 3?
4.Mention the factor pairs of 234?
5.What is the square of 234?
6.How can children in Oman use numbers in everyday life to understand Factors of 234?
7.What are some fun ways kids in Oman can practice Factors of 234 with numbers?
8.What role do numbers and Factors of 234 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of 234 skills?
Important Glossaries for Factors of 234
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 234.
- 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 234 are (1, 234), (2, 117), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 234 is 2 × 3² × 13.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number. For instance, using the multiplication method for 234 gives pairs like (1, 234), (2, 117), etc.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 234
About BrightChamps in Oman
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.
