101 LearnersLast updated on May 26th, 2025
Factors of 268
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 268, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 268?
The numbers that divide 268 evenly are known as factors of 268.
A factor of 268 is a number that divides the number without remainder.
The factors of 268 are 1, 2, 4, 67, 134, and 268.
Negative factors of 268: -1, -2, -4, -67, -134, and -268.
Prime factors of 268: 2 and 67.
Prime factorization of 268: 2² × 67.
The sum of factors of 268: 1 + 2 + 4 + 67 + 134 + 268 = 476
How to Find Factors of 268?
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 268. Identifying the numbers which are multiplied to get the number 268 is the multiplication method.
Step 1: Multiply 268 by 1, 268 × 1 = 268.
Step 2: Check for other numbers that give 268 after multiplying 2 × 134 = 268 4 × 67 = 268
Therefore, the positive factor pairs of 268 are: (1, 268), (2, 134), (4, 67).
All these factor pairs result in 268.
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 a simple division method
Step 1: Divide 268 by 1, 268 ÷ 1 = 268.
Step 2: Continue dividing 268 by the numbers until the remainder becomes 0.
268 ÷ 1 = 268
268 ÷ 2 = 134
268 ÷ 4 = 67
Therefore, the factors of 268 are: 1, 2, 4, 67, 134, 268.
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 268 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
268 ÷ 2 = 134
134 ÷ 2 = 67
67 ÷ 67 = 1
The prime factors of 268 are 2 and 67.
The prime factorization of 268 is: 2² × 67.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 268 is divided by 2 to get 134.
Step 2: Now divide 134 by 2 to get 67.
Step 3: Then divide 67 by 67 to get 1. Here, 67 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 268 is: 2² × 67.
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 268: (1, 268), (2, 134), and (4, 67).
Negative factor pairs of 268: (-1, -268), (-2, -134), and (-4, -67).
Common Mistakes and How to Avoid Them in Factors of 268
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 268, 1 and 268 are also factors.
Factors of 268 Examples
Problem 1
There are 268 apples and 4 baskets. How will they be divided equally?
Each basket will have 67 apples.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets.
268/4 = 67
Problem 2
A garden is rectangular, the length of the garden is 2 meters and the total area is 268 square meters. Find the width?
134 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
268 = 2 × width
To find the value of width, we need to shift 2 to the left side.
268/2 = width
Width = 134.
Problem 3
There are 134 potted plants and 2 shelves. How many plants will be on each shelf?
Each shelf will have 67 plants.
Explanation
To find the plants on each shelf, divide the total plants with the shelves.
134/2 = 67
Problem 4
In a competition, there are 268 participants, and 67 teams. How many participants are there in each team?
There are 4 participants in each team.
Explanation
Dividing the participants with the total teams, we will get the number of participants in each team.
268/67 = 4
Problem 5
268 books need to be arranged in 2 libraries. How many books will go in each library?
Each library will have 134 books.
Explanation
Divide total books with libraries.
268/2 = 134
FAQs on Factors of 268
1.What are the factors of 268?
2.Mention the prime factors of 268.
3.Is 268 a multiple of 4?
4.Mention the factor pairs of 268?
5.What is the square of 268?
Important Glossaries for Factor of 268
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 268 are 1, 2, 4, 67, 134, and 268.
- Prime factors: The factors which are prime numbers. For example, 2 and 67 are prime factors of 268.
- 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 268 are (1, 268), (2, 134), etc
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 268 is 2² × 67.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 268 is a multiple of 4.
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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.
