Factors of 310
2026-02-28 08:42 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without a 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 310, how they are used in real life, and tips to learn them quickly.

What are the Factors of 310?

The numbers that divide 310 evenly are known as factors of 310.

A factor of 310 is a number that divides the number without a remainder.

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, and 310.

Negative factors of 310: -1, -2, -5, -10, -31, -62, -155, and -310.

Prime factors of 310: 2, 5, and 31.

Prime factorization of 310: 2 × 5 × 31.

The sum of factors of 310: 1 + 2 + 5 + 10 + 31 + 62 + 155 + 310 = 576

How to Find Factors of 310?

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 310. Identifying the numbers which are multiplied to get the number 310 is the multiplication method.

Step 1: Multiply 310 by 1, 310 × 1 = 310.

Step 2: Check for other numbers that give 310 after multiplying

2 × 155 = 310

5 × 62 = 310

10 × 31 = 310

Therefore, the positive factor pairs of 310 are: (1, 310), (2, 155), (5, 62), and (10, 31).

All these factor pairs result in 310.

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 a whole number as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 310 by 1, 310 ÷ 1 = 310.

Step 2: Continue dividing 310 by the numbers until the remainder becomes 0.

310 ÷ 1 = 310

310 ÷ 2 = 155

310 ÷ 5 = 62

310 ÷ 10 = 31

Therefore, the factors of 310 are: 1, 2, 5, 10, 31, 62, 155, 310.

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: In this process, prime factors of 310 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

310 ÷ 2 = 155

155 ÷ 5 = 31

31 ÷ 31 = 1

The prime factors of 310 are 2, 5, and 31.

The prime factorization of 310 is: 2 × 5 × 31.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 310 is divided by 2 to get 155.

Step 2: Now divide 155 by 5 to get 31.

Step 3: Here, 31 is a prime number and cannot be divided anymore. So, the prime factorization of 310 is: 2 × 5 × 31.

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 310: (1, 310), (2, 155), (5, 62), and (10, 31).

Negative factor pairs of 310: (-1, -310), (-2, -155), (-5, -62), and (-10, -31).

Common Mistakes and How to Avoid Them in Factors of 310

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 10 workers and 310 boxes. How will they distribute the boxes equally?

Okay, lets begin

They will get 31 boxes each.

Explanation

To divide the boxes equally, we need to divide the total boxes by the number of workers.

310/10 = 31

Well explained 👍

Problem 2

A rectangular garden has a length of 62 meters and a total area of 310 square meters. Find the width?

Okay, lets begin

5 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

310 = 62 × width

To find the value of width, we need to shift 62 to the left side.

310/62 = width

Width = 5.

Well explained 👍

Problem 3

There are 31 jars and 310 candies. How many candies will be in each jar?

Okay, lets begin

Each jar will have 10 candies.

Explanation

To find the candies in each jar, divide the total candies by the jars.

310/31 = 10

Well explained 👍

Problem 4

In a class, there are 310 students, and 62 groups. How many students are there in each group?

Okay, lets begin

There are 5 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

310/62 = 5

Well explained 👍

Problem 5

310 books need to be arranged in 2 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 155 books.

Explanation

Divide total books with shelves.

310/2 = 155

Well explained 👍

FAQs on Factors of 310

1.What are the factors of 310?

1, 2, 5, 10, 31, 62, 155, and 310 are the factors of 310.

2.Mention the prime factors of 310.

The prime factors of 310 are 2 × 5 × 31.

3.Is 310 a multiple of 5?

4.Mention the factor pairs of 310?

(1, 310), (2, 155), (5, 62), and (10, 31) are the factor pairs of 310.

5.What is the square of 310?

Important Glossaries for Factor of 310

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 310 are 1, 2, 5, 10, 31, 62, 155, and 310.
  • Prime Factors: The factors which are prime numbers. For example, 2, 5, and 31 are prime factors of 310.
  • 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 310 are (1, 310), (2, 155), etc.
  • Prime Factorization: The process of breaking down a number into its prime numbers. For example, the prime factorization of 310 is 2 × 5 × 31.
  • Multiplication Method: A technique to find factors by identifying pairs of numbers that multiply to give a target number, like 310.

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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.