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240 LearnersLast updated on December 16, 2025
Factors of -25
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 -25, how they are used in real life, and tips to learn them quickly.
What are the Factors of -25?
The numbers that divide -25 evenly are known as factors of -25.
A factor of -25 is a number that divides the number without remainder.
The factors of 25 are 1, 5, and 25.
Negative factors of 25: -1, -5, and -25.
Prime factors of 25: 5.
Prime factorization of 25: (52).
The sum of factors of 25: 1 + 5 + 25 = 31
| Factor Type | Values |
| Positive Factors of -25 | (1, 5, 25) |
| Negative Factors of -25 | (-1, -5, -25) |
| Prime Factors of -25 | (-5) |
| Prime Factorization of -25 | -52 |
| Sum of factors of -25 | 0 |
How to Find Factors of -25?
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 25. Identifying the numbers which are multiplied to get the number 25 is the multiplication method.
Step 1: Multiply 25 by 1, 25 × 1 = 25.
Step 2: Check for other numbers that give 25 after multiplying 5 × 5 = 25
Therefore, the positive factor pairs of 25 are: (1, 25) and (5, 5).
All these factor pairs result in 25. For every positive factor, there is a negative factor.
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Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 25 by 1, 25 ÷ 1 = 25.
Step 2: Continue dividing 25 by the numbers until the remainder becomes 0.
25 ÷ 1 = 25
25 ÷ 5 = 5
Therefore, the factors of 25 are: 1, 5, 25.
Thus, the factors of -25 include -1, -5, -25.
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 -25
To find the prime factors of 25 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-25 ÷ -5 = -5
-5 ÷ -5 = -1
The prime factor of -25 is -5.
Prime Factorization of -25
Prime Factorization breaks down the prime factors of -25.
Step 1: Firstly, -25 is divided by 5 to get 5.
Step 2: Now divide 5 by 5 to get 1. Here, 5 is the prime number that cannot be divided anymore.
So, the prime factorization of 25 is: (52).
Factor Tree of -25
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of -25
The factors of -25 can be written in both positive and negative pairs. The table below represents the factor pairs of -25, where the product of each pair of numbers is equal to -25.
Positive Pair Factors of -25:
| Factors | Positive Pair Factors |
| 1 × 25 = 25 | 1, 25 |
| 5 × 5 = 25 | 5, 5 |
Since the product of two negative numbers is also positive, -25 also has negative pair factors.
Negative Pair Factors of -25:
| Factors | Negative Pair Factors |
| -1 × -25 = -25 | −1, -25 |
| -5 × -5 = -25 | -5, -5 |
Common Mistakes and How to Avoid Them in Factors of -25
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -25, 1, and -25 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -25 consist of -1, -5, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 25/1.5 ≈ 16.67, 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 25 are prime numbers. For example, 5 is the prime factor of 25, but it has other factors like 1, 25.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 25 as 52 and missing all the key factors.
Factors of -25 Examples
Problem 1
There are 5 friends and 25 apples. How will they divide them equally?
They will get 5 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of friends.
25/5 = 5
Problem 2
A garden is square-shaped, and the total area is 25 square meters. What is the length of each side?
5 meters.
Explanation
For a square, the area is calculated as: Area = side × side
25 = side × side
To find the side length, we find the square root of 25.
The side = 5.
Problem 3
A Walmart store in Chicago issues a refund correction of โ$25 on a customerโs grocery bill due to a billing error. For accounting verification, the manager wants to list all integer factors of โ25 that could be used to split or trace the adjustment amount across system logs. What are the factors of โ25?
−1, −5, −25, 1, 5, 25
Explanation
Factors of −25 are all integers that multiply to give −25.
Since the result is negative, one factor must be positive and the other negative.
The positive factors of 25 are: 1, 5, 25
Pairing them with negative signs gives:
−1 × 25 = −25
−5 × 5 = −25
−25 × 1 = −25
So, all integer factors of −25 are −1, −5, −25, 1, 5, and 25.
Problem 4
An NBA game in Los Angeles (LA) was canceled, and a sports app records a โ$25 adjustment per ticket in its refund system. To test the system, developers list all integer factors of โ25 that could represent valid multiplier pairs for reversing the transaction. Find the factors of โ25.
−1, −5, −25, 1, 5, 25
Explanation
To find the factors of −25, we look for all integer pairs whose product is −25.
The number 25 has factors: 1, 5, and 25.
Making one number negative in each pair gives:
1 × −25
5 × −5
25 × −1
Including both positive and negative integers, the full set of factors is −1, −5, −25, 1, 5, and 25.
Problem 5
After an NFL game in Dallas, a team bus log shows a fuel accounting error of โ25 gallons due to overestimation. The loss must be split evenly across multiple fuel entries. What are all the factors of โ25 that represent valid equal splits?
−1, −5, −25, 1, 5, 25
Explanation
Factors of −25 are integers that divide −25 exactly.
Because −25 is negative, valid factor pairs must include one positive and one negative number.
These pairs give the full factor list: ±1, ±5, ±25.
FAQs on Factors of -25
1.What are the factors of -25?
2.Mention the prime factor of 25.
3.Is 25 a multiple of 5?
4.Mention the factor pairs of -25?
5.What is the square of 25?
6.What is the smallest factor of โ25?
7.What is the largest factor of โ25?
8.How many even factors does โ25 have?
9.What are the odd factors of โ25?
10.What is the sum of all the factors of โ25?
Important Glossaries for Factors of -25
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -25 are 1, 5, 25, -1, -5, -25.
- Prime factors: The factors which are prime numbers. For example, 5 is a prime factor of 25.
- 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 -25 are (1, 25), (-1, -25), etc.
- Multiplication method: A method used to find factors by determining the product pairs that result in the original number.
- Division method: A method to find factors by dividing the number with whole numbers to find those that result in a whole quotient.
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.
