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224 LearnersLast updated on December 17, 2025
Factors of 313
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 313, how they are used in real life, and tips to learn them quickly.
What are the Factors of 313?
The numbers that divide 313 evenly are known as factors of 313.
A factor of 313 is a number that divides the number without remainder.
The factors of 313 are 1 and 313.
Negative factors of 313: -1 and -313.
Prime factors of 313: 313 is a prime number and has no other prime factors.
The sum of factors of 313: 1 + 313 = 314
| Factor Type | Values |
| Positive Factors of 313 | (1, 313) |
| Negative Factors of 313 | (-1, -313) |
| Prime Factors of 313 | (1, 313) |
| Prime Factorization of 313 | 1 × 313 |
| Sum of factors of 313 | 314 |
How to Find Factors of 313?
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 313.
Since 313 is a prime number, the only multiplication that results in 313 is multiplying it by 1.
Step 1: Multiply 313 by 1, 313 × 1 = 313.
There are no other pairs, as 313 is a prime number.
Therefore, the positive factor pair of 313 is: (1, 313).
For every positive factor, there is a negative factor.
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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 313 by 1, 313 ÷ 1 = 313.
Step 2: Checking further, 313 is not divisible by any other number without leaving a remainder.
Therefore, the factors of 313 are: 1 and 313.
Prime Factors and Prime Factorization
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime Factors of 313
Since 313 is a prime number, it is only divisible by 1 and itself.
Hence, the prime factors are 1 and 313.
Prime Factorization of 313
Prime Factorization breaks down the prime factors of 313.
Expressed as 1 × 313
Factor Tree of 313
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of 313
Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pair of 313:
| Factors | Positive Pair Factors |
| 1 × 313 = 313 | 1, 313 |
Negative factor pair of 313:
| Factors | Negative Pair Factors |
| −1 × −313 = 313 | −1, −313 |
Common Mistakes and How to Avoid Them in Factors of 313
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 313, 1 and 313 are the factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 313 include -1 and -313.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 313/1.5 = 208.6667, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all factors of 313 are prime numbers. For 313, the prime factor is itself, but its factors include 1.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and write incorrect factors.
For example, not recognizing that 313 is 313 × 1 and missing it as a prime factorization.
Factors of 313 Examples
Problem 1
A scientist has 313 samples and wants to divide them equally into containers. How many containers can they use to ensure an equal number of samples in each?
They can use 1 or 313 containers.
Explanation
To divide the samples equally, we need to use the factors of 313.
The factors are 1 and 313, meaning they can use either 1 container with 313 samples or 313 containers with 1 sample each.
Problem 2
A garden plot is 313 square meters. If the width is 1 meter, what is the length?
313 meters.
Explanation
To find the length of the garden plot, use the formula:
Area = length × width
313 = 1 × length
Length = 313.
Problem 3
A Walmart store in New York City is reviewing a grocery bill and sales-tax entry. The final amount recorded is $313, and the accounting team wants to know how many equal whole-dollar groups this amount can be split into without leaving any remainder. What are the factors of 313?
1, 313
Explanation
To find the factors of 313, check which numbers divide it exactly.
313 cannot be divided evenly by 2, 3, 5, 7, or any other smaller integers.
Since 313 has no divisors other than 1 and itself, it is a prime number.
Therefore, the only factors of 313 are 1 and 313.
Problem 4
In a Boston school science lab, students analyze medicine inventory similar to records used by CVS pharmacies. A sample contains 313 mg of a compound and must be divided into equal integer doses with no leftovers. Which numbers are factors of 313?
1, 313
Explanation
A factor divides 313 evenly with no remainder.
When testing all possible divisors, none divide 313 except 1 and 313 itself.
This confirms that 313 is a prime number, so it has exactly two factors.
Problem 5
An NBA team in Los Angeles (LA) reviews travel expenses after a road game in San Francisco. Based on gas prices per gallon, the team logs 313 gallons of fuel usage that must be split evenly across fuel records. What are the factors of 313 that allow an exact split?
1, 313
Explanation
For an even split, the number of groups must divide 313 without a remainder.
Because 313 is a prime number, it cannot be divided evenly into smaller whole groups.
The only possible equal splits are 1 group of 313 gallons or 313 groups of 1 gallon, making 1 and 313 the only factors.
FAQs on Factors of 313
1.What are the factors of 313?
2.Mention the prime factors of 313.
3.Is 313 a multiple of 2?
4.Mention the factor pairs of 313?
5.Is 313 a prime number?
6.How many factors does 313 have?
7.What is the smallest factor of 313?
8.What is the largest factor of 313?
9.Which factors of 313 add up to 13?
10.How many even factors does 313 have?
11.What are the odd factors of 313?
12.What is the sum of all the factors of 313?
Important Glossaries for Factors of 313
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 313 are 1 and 313.
- Prime factors: The factors which are prime numbers. For example, 313 is a prime factor of itself.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 313 is (1, 313).
- Prime number: A number greater than 1 with no divisors other than 1 and itself. 313 is an example of a prime number.
- Negative factors: Factors that are negative. For example, -1 and -313 are negative factors of 313.
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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.
