117 LearnersLast updated on May 26th, 2025
Factors of 100
Factors are the numbers that divide any given number evenly without a 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 100, how they are used in real life, and 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.
Negative factors of 100: -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 factors of 100: 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 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.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as 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.
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 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.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 100 is divided by 2 to get 50.
Step 2: Now divide 50 by 2 to get 25.
Step 3: 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).
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 word. Always remember to include 1 and the number itself. For example, in factors of 100, 1 and 100 are also factors.
Factors of 100 Examples
Problem 1
There are 10 friends and 100 candies. How will they divide it equally?
They will get 10 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
100/10 = 10
Problem 2
A rectangle has a length of 10 meters and a total area of 100 square meters. Find the width.
10 meters.
Explanation
To find the width of the rectangle, we use the formula,
Area = length × width
100 = 10 × width
To find the value of width, we need to shift 10 to the left side.
100/10 = width
Width = 10.
Problem 3
There are 25 boxes and 100 items. How many items will be in each box?
Each box will have 4 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
100/25 = 4
Problem 4
In a class, there are 100 students and 5 teams. How many students are there in each team?
There are 20 students in each team.
Explanation
Dividing the students by the total teams, we will get the number of students in each team.
100/5 = 20
Problem 5
100 books need to be arranged on 4 shelves. How many books will go on each shelf?
Each shelf will have 25 books.
Explanation
Divide total books by shelves.
100/4 = 25
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?
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, and 100.
- 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.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 100 is 2² × 5².
- Multiples: A multiple of a number is the product of that number and an integer. For example, 100 is a multiple of 4 because 4 × 25 = 100.
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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.
