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219 LearnersLast updated on December 17, 2025
Factors of -100
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of -100, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -100?
The numbers that divide -100 evenly are known as factors of -100.
A factor of -100 is a number that divides the number without remainder.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Since we need factors of -100, we also consider their negative counterparts: -1, -2, -4, -5, -10, -20, -25, -50, and -100.
Prime factors of 100: 2 and 5.
Prime factorization of 100: 22 × 52.
The sum of positive factors of 100: 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217
| Factor Type | Values |
| Positive Factors of -100 | (1, 2, 4, 5, 10, 20, 25, 50, 100) |
| Negative Factors of -100 | (-1, -2, -4, -5, -10, -20, -25, -50, -100) |
| Prime Factors of -100 | (2, 5) |
| Prime Factorization of -100 | 22 × 52 |
| Sum of factors of -100 | 217 |
How to Find Factors of -100?
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 100. Identifying the numbers which are multiplied to get the number 100 is the multiplication method.
Step 1: Multiply 100 by 1, 100 × 1 = 100.
Step 2: Check for other numbers that give 100 after multiplying
2 × 50 = 100
4 × 25 = 100
5 × 20 = 100
10 × 10 = 100
Therefore, the positive factor pairs of 100 are: (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).
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 a simple division method
Step 1: Divide 100 by 1, 100 ÷ 1 = 100.
Step 2: Continue dividing 100 by the numbers until the remainder becomes 0.
100 ÷ 1 = 100
100 ÷ 2 = 50
100 ÷ 4 = 25
100 ÷ 5 = 20
100 ÷ 10 = 10
Therefore, the factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Considering -100, we include their negatives as well: -1, -2, -4, -5, -10, -20, -25, -50, -100.
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 100
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 100 are 2 and 5.
Prime Factorization of -100
Prime Factorization breaks down the prime factors of -100.
Step 1: Firstly, 100 is divided by 2 to get 50.
Step 2: Now divide 50 by 2 to get 25.
Step 3: Then divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 100 is: 22 × 52.
Factor Tree of -100
The factor tree is the graphical representation of breaking down any number into prime factors.
Factor Pairs of -100
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 -100:
| Factors | Positive Pair Factors |
| 1 × −100 = −100 | 1, −100 |
| 2 × −50 = −100 | 2, −50 |
| 4 × −25 = −100 | 4, −25 |
| 5 × −20 = −100 | 5, −20 |
| 10 × −10 = −100 | 10, −10 |
Negative factor pairs of -100:
| Factors | Negative Pair Factors |
| −1 × 100 = −100 | −1, 100 |
| −2 × 50 = −100 | −2, 50 |
| −4 × 25 = −100 | −4, 25 |
| −5 × 20 = −100 | −5, 20 |
| −10 × 10 = −100 | −10, 10 |
Common Mistakes and How to Avoid Them in Factors of -100
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 -100, 1 and -100 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of -100 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -100/1.5 = -66.666, 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 -100 are prime numbers.
For example, 2 and 5 are the prime factors of 100, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, Not breaking 100 as 22 × 52 and missing all the key factors.
Factors of -100 Examples
Problem 1
There are 10 teams and -100 points to distribute equally. How many points will each team get?
Each team will get -10 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
-100/10 = -10
Problem 2
A garden is rectangular, the length of the garden is 20 meters and the total area is -100 square meters. Find the width?
-5 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
-100 = 20 × width
To find the value of width, we need to shift 20 to the left side.
-100/20 = width
Width = -5.
Problem 3
A Target store in Los Angeles (LA) finds a checkout error while reconciling grocery bills and sales tax. The system shows a โ100 USD adjustment that must be split into equal whole-dollar corrections across departments. What are all the factors of โ100 that represent possible equal splits?
−1, −2, −4, −5, −10, −20, −25, −50, −100, 1, 2, 4, 5, 10, 20, 25, 50, 100
Explanation
First list the factors of 100 using its prime factorization:
100 = 2² × 5².
All positive divisors come from combinations of these primes.
Because the original number is negative, each positive factor also has a negative counterpart.
Together, these make the full set of factors of −100.
Problem 4
In a Boston school science lab, students analyze pharmacy inventory data similar to CVS systems. A simulated entry shows a โ100 mg correction in medicine dosage that must be divided into equal integer units. Which integers are factors of โ100?
−1, −2, −4, −5, −10, −20, −25, −50, −100, 1, 2, 4, 5, 10, 20, 25, 50, 100
Explanation
A factor divides −100 evenly with no remainder.
The absolute value 100 has multiple divisors from 2² × 5².
Since the correction is negative, both positive and negative integers qualify.
All such integers form the factor list of −100.
Problem 5
An NFL team in Dallas reviews travel expenses after a game in Houston. Due to a gas-price correction (per gallon), the fuel log shows a โ100 gallon adjustment that must be split evenly across records. What are all the factors of โ100 that allow an exact split?
−1, −2, −4, −5, −10, −20, −25, −50, −100, 1, 2, 4, 5, 10, 20, 25, 50, 100
Explanation
Equal division requires integers that divide −100 without leaving a remainder.
The number 100 has several factor pairs.
Because the total adjustment is negative, each positive divisor also has a corresponding negative divisor.
Thus, all ± divisors of 100 are valid factors of −100.
FAQs on Factors of -100
1.What are the factors of -100?
2.Mention the prime factors of -100.
3.Is -100, a multiple of 4?
4.Mention the factor pairs of -100?
5.What is the square of -100?
6.How many factors does โ100 have?
7.What is the smallest factor of โ100?
8.What is the largest factor of โ100?
9.Which factors of โ100 add up to 13?
10.How many even factors does โ100 have?
11.What are the odd factors of โ100?
12.What is the sum of all the factors of โ100?
Important Glossaries for Factors of -100
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -100 are 1, 2, 4, 5, 10, 20, 25, 50, 100 and their negatives.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 100.
- 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 -100 are (1, -100), (2, -50), etc.
- Negative Factors: These are factors of a number that are negative whole numbers. For -100, they include -1, -2, -4, etc.
- Prime Factorization: The expression of a number as the product of its prime factors. For 100, it's 2^2 × 5^2.
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.
