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295 LearnersLast updated on December 12, 2025
Factors of -31
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
- Using factor tree
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.
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 -31, 1 and -31 are also 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 -31 include -1 and -31.
Mistake 3
Including the Fraction
Children might sometimes mistakenly include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because -31/1.5 = -20.666, 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 -31 are prime numbers. While 31 is a prime factor, factors include 1 and -1 as well.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not recognizing -1 × 31 as a factorization and missing key factors.
Factors of -31 Examples
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?
1 or 31 people
Explanation
Since -31 is a prime number, it can only be divided evenly by 1 or 31.
Problem 2
A debt of -31 dollars is to be split among 31 friends. How much does each friend owe?
Each friend owes -1 dollar.
Explanation
To split the debt equally, divide the total debt by the number of friends.
-31/31 = -1
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?
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.
FAQs on Factors of -31
1.What are the factors of -31?
2.Mention the prime factors of -31.
3.Is -31 a multiple of -1?
4.Mention the factor pairs of -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.
Samia
About the Author
Samia 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.
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