Factors of -31
2026-02-28 11:57 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-31

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Last updated on December 12, 2025

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 -31, how they are used in real life, and the tips to learn them quickly.

What are the Factors of -31?

The numbers that divide -31 evenly are known as factors of -31.

A factor of -31 is a number that divides the number without remainder.

The factors of -31 are 1 and 31.

Negative factors of -31: -1 and -31.

Prime factors of -31: 31.

Prime factorization of -31: -1 × 31.

The sum of factors of -31: 1 + 31 + (-1) + (-31) = 0

How to Find Factors of -31?

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 -31. Identifying the numbers which are multiplied to get the number -31 is the multiplication method.

Step 1: Multiply -31 by 1, -31 × 1 = -31.

Step 2: Check for other numbers that give -31 after multiplying -1 × 31 = -31

Therefore, the factor pairs of -31 are: (1, -31) and (-1, 31).

All these factor pairs result in -31.

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Finding Factors Using Division Method

Dividing the given number by whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following a simple division method 

Step 1: Divide -31 by 1, -31 ÷ 1 = -31.

Step 2: Continue dividing -31 by numbers until the remainder becomes 0.

-31 ÷ 1 = -31

-31 ÷ -1 = 31

Therefore, the factors of -31 are: 1, -1, 31, and -31.

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 -31 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

Since -31 is a prime number, it can only be divided by 1 and itself.

The prime factorization of -31 is: -1 × 31.

Factor Tree

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

As -31 is a prime number, it does not break further like composite numbers. It can only be represented as -1 × 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.

Factor pairs of -31: (1, -31) and (-1, 31).

Common Mistakes and How to Avoid Them in Factors of -31

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

Problem 1

A group of people needs to distribute -31 tokens evenly among themselves. If each person should receive a whole number of tokens, how many people can be in the group?

Okay, lets begin

1 or 31 people

Explanation

Since -31 is a prime number, it can only be divided evenly by 1 or 31.

Well explained 👍

Problem 2

A debt of -31 dollars is to be split among 31 friends. How much does each friend owe?

Okay, lets begin

Each friend owes -1 dollar.

Explanation

To split the debt equally, divide the total debt by the number of friends.

-31/31 = -1

Well explained 👍

Problem 3

A project requires -31 hours of work, which can only be handled by a single person or an entire team. If a team takes on the project, how many members should it have so each member contributes whole hours?

Okay, lets begin

The team should have 1 or 31 members.

Explanation

Because -31 is a prime number, the work can only be divided among 1 or 31 members to maintain whole hours.

Well explained 👍

FAQs on Factors of -31

1.What are the factors of -31?

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

2.Mention the prime factors of -31.

The prime factor of -31 is 31.

3.Is -31 a multiple of -1?

4.Mention the factor pairs of -31?

The factor pairs of -31 are (1, -31) and (-1, 31).

5.What is the absolute value of -31?

Important Glossaries for Factors of -31

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -31 are 1, -1, 31, and -31.
  • Prime factors: The factors which are prime numbers. For example, 31 is the prime factor of -31.
  • 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 -31 are (1, -31) and (-1, 31).
  • Negative factors: Factors that are negative numbers. For example, -1 and -31 are negative factors of -31.
  • Prime number: A number greater than 1 with no divisors other than 1 and itself. For example, 31 is a prime number.

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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.