Factors of 31
2026-02-28 17:38 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-31

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Last updated on December 11, 2025

What is a factor of a number? The factor of a number is the numbers when multiplied the product will be the number. We use it in our daily life for distribution of any objects and money exchange.

What are the factors of 31?

The factor of 31 is the number when multiplied, giving 31 as product. The factors of 31 are 1 and 31. 

Negative factors of 31: Factors of a number can be both positive and negative. The negative factors of a number are the negative counterpart of the positive factors. So, the negative factors of 31 are -1 and -31.

Prime factors of 31: As 31 is a prime number, the prime factors of 31 are 1 and 31.

How to find the factors of 31

There are different methods to find the factors. Some methods commonly used are

  • Multiplication method
  • Division method
  • Prime factors and prime factorization
  • Factor tree
     

Finding factors using multiplication

The pair of numbers when multiplied gives the 31 as a product.  Follow the steps to find the factors of 31

Step 1: Find all numbers whose product is 31


1 × 31 = 31


Step 2:  pair them up and make a list of it

         Factors of 31 are (1, 31)

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Finding factors by division method

In the division method, we need to check which numbers can evenly divide 31. 

Let’s check the factors of 31 using division method:

31 / 1 =31

Prime factors and prime factorization

Prime factorization of a number is dividing the number into small factors. The product of the prime factors will be the number itself. 

As 31 is a prime number, the prime factors of 31 are 1 and 31.
 

Factor tree

The pictorial representation of prime factorization is a factor tree. Here each branch splits into prime factors. 

Factor pairs: As the name, factor pairs are the pair of numbers and the product of the pair would be the number itself

Positive factor pairs of 31: (1, 31)


Negative factor pairs of 31: (-1, -31)

Common mistakes and how to avoid them in factors of 31

some common mistakes with their solutions are given below:

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Problem 1

List out all the prime factors of 31?

Okay, lets begin

 As 31 is a prime number, the prime factors of 31 are 1 and 31.
 

Explanation

prime numbers have only two factors, i.e., one and the number itself.
 

Well explained 👍

Problem 2

Check whether 31 is a factor of 62.

Okay, lets begin

When we divide 62 by 31 the quotient is 2. Hence, yes 31 a factor of 62.

Explanation

Since 31 evenly divides 62, 31 is a factor of 62.

Well explained 👍

Problem 3

List out all the negative factors of 31?

Okay, lets begin

The negative factors of 31 are -1 and -31.
 

Explanation

 the negative factors of a number are the negative counterparts of the positive factors.

Well explained 👍

FAQs on factors of 31

1.How many factors does 31 have?

The number 31 has 2 factors. 1 and 31 are the factors.
 

2.Check whether 31 a prime or composite number?

Since, 31 has only two factors, i.e, 1 and 31. 31 is a prime number.

3.List down the multiples of 31

The multiples of 31 are 31, 62, 93, 124, 155, 186, 217, 248, 279, 310,…
 

Important glossaries for factor 31

  • Prime numbers: Any number which can only divisible by one and the number itself is a prime number.
  • Composite numbers: The numbers other than prime are composite numbers. They have more than two factors.
  • Factor tree: The pictorial representation of factors of a number.
  • Quotient: The result when dividing two numbers. For example, when we divide 6 by 2, the quotient is 3
     

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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.