116 LearnersLast updated on May 26th, 2025
Factors of 262
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 262, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 262?
The numbers that divide 262 evenly are known as factors of 262.
A factor of 262 is a number that divides the number without remainder.
The factors of 262 are 1, 2, 131, and 262.
Negative factors of 262: -1, -2, -131, and -262.
Prime factors of 262: 2 and 131.
Prime factorization of 262: 2 × 131.
The sum of factors of 262: 1 + 2 + 131 + 262 = 396
How to Find Factors of 262?
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 262. Identifying the numbers which are multiplied to get the number 262 is the multiplication method.
Step 1: Multiply 262 by 1, 262 × 1 = 262.
Step 2: Check for other numbers that give 262 after multiplying
2 × 131 = 262
Therefore, the positive factor pairs of 262 are: (1, 262) and (2, 131). All these factor pairs result in 262. 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 262 by 1, 262 ÷ 1 = 262.
Step 2: Continue dividing 262 by the numbers until the remainder becomes 0.
262 ÷ 1 = 262
262 ÷ 2 = 131
Therefore, the factors of 262 are: 1, 2, 131, and 262.
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 262 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
262 ÷ 2 = 131
131 ÷ 131 = 1
The prime factors of 262 are 2 and 131.
The prime factorization of 262 is: 2 × 131.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 262 is divided by 2 to get 131.
Step 2: Now divide 131 by 131 to get 1.
Here, 131 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 262 is: 2 × 131.
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 262: (1, 262) and (2, 131).
Negative factor pairs of 262: (-1, -262) and (-2, -131).
Common Mistakes and How to Avoid Them in Factors of 262
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 262, 1 and 262 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 262 consist of -1, -2, -131, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 262/1.5 = 174.666, 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 262 are prime numbers. For example, 2 and 131 are the prime factors of 262, but it has other factors like 1, 262.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 262 as 2 × 131 and missing all the key factors.
Factors of 262 Examples
Problem 1
There are 2 teams and 262 apples. How will they divide it equally?
They will get 131 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams.
262/2 = 131
Problem 2
A garden is rectangular, the length of the garden is 2 meters and the total area is 262 square meters. Find the width?
131 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
262 = 2 × width
To find the value of width, we need to shift 2 to the left side.
262/2 = width
Width = 131.
Problem 3
There are 131 bags and 262 marbles. How many marbles will be in each bag?
Each bag will have 2 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the number of bags.
262/131 = 2
Problem 4
In a class, there are 262 students, and 131 groups. How many students are there in each group?
There are 2 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
262/131 = 2
Problem 5
262 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 131 books.
Explanation
Divide total books by shelves.
262/2 = 131
FAQs on Factors of 262
1.What are the factors of 262?
2.Mention the prime factors of 262.
3.Is 262 a multiple of 2?
4.Mention the factor pairs of 262?
5.What is the square of 262?
Important Glossaries for Factor of 262
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 262 are 1, 2, 131, and 262.
- Prime factors: The factors which are prime numbers. For example, 2 and 131 are prime factors of 262.
- 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 262 are (1, 262) and (2, 131).
- Multiplication method: A method to find factors by identifying pairs that multiply to the target number. For example, 2 × 131 = 262.
- Division method: A method to find factors by dividing the number by integers until no remainder exists. For example, 262 ÷ 2 = 131.
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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.
