120 LearnersLast updated on May 26th, 2025
Factors of 258
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 258, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 258?
The numbers that divide 258 evenly are known as factors of 258.
A factor of 258 is a number that divides the number without remainder.
The factors of 258 are 1, 2, 3, 6, 43, 86, 129, and 258.
Negative factors of 258: -1, -2, -3, -6, -43, -86, -129, and -258.
Prime factors of 258: 2, 3, and 43.
Prime factorization of 258: 2 × 3 × 43.
The sum of factors of 258: 1 + 2 + 3 + 6 + 43 + 86 + 129 + 258 = 528
How to Find Factors of 258?
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 258. Identifying the numbers which are multiplied to get the number 258 is the multiplication method.
Step 1: Multiply 258 by 1, 258 × 1 = 258.
Step 2: Check for other numbers that give 258 after multiplying
2 × 129 = 258
3 × 86 = 258
6 × 43 = 258
Therefore, the positive factor pairs of 258 are: (1, 258), (2, 129), (3, 86), (6, 43). All these factor pairs result in 258. For every positive factor, there is a negative factor.
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 the simple division method -
Step 1: Divide 258 by 1, 258 ÷ 1 = 258.
Step 2: Continue dividing 258 by the numbers until the remainder becomes 0.
258 ÷ 1 = 258
258 ÷ 2 = 129
258 ÷ 3 = 86
258 ÷ 6 = 43
Therefore, the factors of 258 are: 1, 2, 3, 6, 43, 86, 129, 258.
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 258 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
258 ÷ 2 = 129
129 ÷ 3 = 43
43 ÷ 43 = 1
The prime factors of 258 are 2, 3, and 43.
The prime factorization of 258 is: 2 × 3 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 258 is divided by 2 to get 129.
Step 2: Now divide 129 by 3 to get 43.
Step 3: Finally, divide 43 by 43 to get 1.
So, the prime factorization of 258 is: 2 × 3 × 43.
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 258: (1, 258), (2, 129), (3, 86), (6, 43).
Negative factor pairs of 258: (-1, -258), (-2, -129), (-3, -86), (-6, -43).
Common Mistakes and How to Avoid Them in Factors of 258
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 number. Always remember to include 1 and the number itself.
For example, in factors of 258, 1 and 258 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 258 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 258/1.5 = 172, 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 258 are prime numbers. For example, 2, 3, and 43 are the prime factors of 258, but it has other factors like 6, 86.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 258 as 2 × 3 × 43 and missing all the key factors.
Factors of 258 Examples
Problem 1
There are 6 bicycles and 258 wheels. How many wheels are on each bicycle?
Each bicycle has 43 wheels.
Explanation
To find the wheels on each bicycle, we need to divide the total wheels by the number of bicycles.
258/6 = 43
Problem 2
A rectangular garden has a width of 3 meters, and the total area is 258 square meters. What is the length of the garden?
86 meters.
Explanation
To find the length of the garden, we use the formula, Area = length × width
258 = length × 3
To find the value of length, we need to divide 258 by 3.
258/3 = length
Length = 86.
Problem 3
There are 129 apples and 2 baskets. How many apples will be in each basket?
Each basket will have 64 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
258/2 = 129
Problem 4
A school has 258 students, and they are divided into 43 teams. How many students are there in each team?
There are 6 students in each team.
Explanation
Dividing the students by the total teams, we will get the number of students in each team.
258/43 = 6
Problem 5
A library has 258 books that need to be arranged in 43 shelves. How many books will go on each shelf?
Each of the shelves has 6 books.
Explanation
Divide total books by shelves.
258/43 = 6
FAQs on Factors of 258
1.What are the factors of 258?
2.Mention the prime factors of 258.
3.Is 258 a multiple of 3?
4.Mention the factor pairs of 258?
5.What is the square of 258?
Important Glossaries for Factors of 258
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 258 are 1, 2, 3, 6, 43, 86, 129, and 258.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 43 are prime factors of 258.
- 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 258 are (1, 258), (2, 129), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For 258, it is 2 × 3 × 43.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, -6, -43, -86, -129, and -258 are the negative factors of 258.
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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.
