Last updated on May 26th, 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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with a prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, 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.
The prime factorization of 100 is: 22 × 52.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
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 Pairs 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: (1, -100), (2, -50), (4, -25), (5, -20), and (10, -10).
Negative factor pairs of -100: (-1, 100), (-2, 50), (-4, 25), (-5, 20), and (-10, 10).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 10 teams and -100 points to distribute equally. How many points will each team get?
Each team will get -10 points.
To distribute the points equally, we need to divide the total points by the number of teams.
-100/10 = -10
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.
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.
There are 25 boxes and -100 candies. How many candies will be in each box?
Each box will have -4 candies.
To find the candies in each box, divide the total candies by the boxes.
-100/25 = -4
In a class, there are -100 students, and 5 groups. How many students are there in each group?
There are -20 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
-100/5 = -20
-100 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has -25 books.
Divide total books by shelves.
-100/4 = -25
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.
: She loves to read number jokes and games.