Factors of -100
2026-02-28 01:07 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-100

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Last updated on December 17, 2025

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.

Problem 1

There are 10 teams and -100 points to distribute equally. How many points will each team get?

Okay, lets begin

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

Well explained 👍

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?

Okay, lets begin

-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.

Well explained 👍

Problem 3

A Target store in Los Angeles (LA) finds a checkout error while reconciling grocery bills and sales tax. The system shows a −100 USD adjustment that must be split into equal whole-dollar corrections across departments. What are all the factors of −100 that represent possible equal splits?

Okay, lets begin

−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.

Well explained 👍

Problem 4

In a Boston school science lab, students analyze pharmacy inventory data similar to CVS systems. A simulated entry shows a −100 mg correction in medicine dosage that must be divided into equal integer units. Which integers are factors of −100?

Okay, lets begin

−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.

Well explained 👍

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 −100 gallon adjustment that must be split evenly across records. What are all the factors of −100 that allow an exact split?

Okay, lets begin

−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.

Well explained 👍

FAQs on Factors of -100

1.What are the factors of -100?

1, 2, 4, 5, 10, 20, 25, 50, 100 and their negative counterparts are the factors of -100.

2.Mention the prime factors of -100.

The prime factors of 100 are 2^2 × 5^2.

3.Is -100, a multiple of 4?

4.Mention the factor pairs of -100?

(1, -100), (2, -50), (4, -25), (5, -20), and (10, -10) are the positive factor pairs of -100.

5.What is the square of -100?

6.How many factors does −100 have?

−100 has 18 factors (including both positive and negative factors).

7.What is the smallest factor of −100?

The smallest factor of −100 is −100.

8.What is the largest factor of −100?

The highest factor of −100 is 100.

9.Which factors of −100 add up to 13?

There are no factors of −100 that add up to 13.

10.How many even factors does −100 have?

−100 has 12 even factors.

11.What are the odd factors of −100?

The odd factors of −100 are −1, 1, −5, 5, −25, and 25.

12.What is the sum of all the factors of −100?

The sum of all the factors of −100 is 0.

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.

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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.