176 LearnersLast updated on May 26th, 2025
Factors of 900
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 900, how they are used in real life, and tips to learn them quickly.
What are the Factors of 900?
The numbers that divide 900 evenly are known as factors of 900. A factor of 900 is a number that divides the number without remainder. The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900.
Negative factors of 900: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -300, -450, and -900.
Prime factors of 900: 2, 3, and 5.
Prime factorization of 900: 2² × 3² × 5².
The sum of factors of 900: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 + 900 = 2970
How to Find Factors of 900?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 900. Identifying the numbers which are multiplied to get the number 900 is the multiplication method.
Step 1: Multiply 900 by 1, 900 × 1 = 900.
Step 2: Check for other numbers that give 900 after multiplying
2 × 450 = 900
3 × 300 = 900
4 × 225 = 900
5 × 180 = 900
6 × 150 = 900
9 × 100 = 900
10 × 90 = 900
12 × 75 = 900
15 × 60 = 900
18 × 50 = 900
20 × 45 = 900
25 × 36 = 900
30 × 30 = 900
Therefore, the positive factor pairs of 900 are: (1, 900), (2, 450), (3, 300), (4, 225), (5, 180), (6, 150), (9, 100), (10, 90), (12, 75), (15, 60), (18, 50), (20, 45), (25, 36), and (30, 30). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as a whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 900 by 1, 900 ÷ 1 = 900.
Step 2: Continue dividing 900 by the numbers until the remainder becomes 0.
900 ÷ 1 = 900
900 ÷ 2 = 450
900 ÷ 3 = 300
900 ÷ 4 = 225
900 ÷ 5 = 180
900 ÷ 6 = 150
900 ÷ 9 = 100
900 ÷ 10 = 90
900 ÷ 12 = 75
900 ÷ 15 = 60
900 ÷ 18 = 50
900 ÷ 20 = 45
900 ÷ 25 = 36
900 ÷ 30 = 30
Therefore, the factors of 900 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900.
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 900 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 900 are 2, 3, and 5. The prime factorization of 900 is: 2² × 3² × 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, 900 is divided by 2 to get 450.
Step 2: Now divide 450 by 2 to get 225.
Step 3: Then divide 225 by 3 to get 75.
Step 4: Divide 75 by 3 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 900 is: 2² × 3² × 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 900: (1, 900), (2, 450), (3, 300), (4, 225), (5, 180), (6, 150), (9, 100), (10, 90), (12, 75), (15, 60), (18, 50), (20, 45), (25, 36), and (30, 30).
- Negative factor pairs of 900: (-1, -900), (-2, -450), (-3, -300), (-4, -225), (-5, -180), (-6, -150), (-9, -100), (-10, -90), (-12, -75), (-15, -60), (-18, -50), (-20, -45), (-25, -36), and (-30, -30).
Common Mistakes and How to Avoid Them in Factors of 900
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 900, 1 and 900 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 900 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor. For example, thinking 1.5 as a factor, because 900/1.5 = 600, 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 900 are prime numbers. For example, 2, 3, and 5 are the prime factors of 900, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 900 as 2² × 3² × 5² and missing all the key factors.
Factors of 900 Examples
Problem 1
There are 9 teams and 900 points. How will they divide the points equally?
They will get 100 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
900/9 = 100
Problem 2
A rectangular garden has a length of 30 meters and a total area of 900 square meters. Find the width.
30 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
900 = 30 × width
To find the value of width, we need to shift 30 to the left side.
900/30 = width
Width = 30.
Problem 3
There are 18 baskets and 900 apples. How many apples will be in each basket?
Each basket will have 50 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
900/18 = 50
Problem 4
In a conference, there are 900 participants, and 9 discussion tables. How many participants are there at each table?
There are 100 participants at each table.
Explanation
Dividing the participants by the total tables, we will get the number of participants at each table.
900/9 = 100
Problem 5
900 chairs need to be arranged in 10 rows. How many chairs will go in each row?
Each of the rows has 90 chairs.
Explanation
Divide total chairs by rows.
900/10 = 90
FAQs on Factors of 900
1.What are the factors of 900?
2.Mention the prime factors of 900.
3.Is 900 a multiple of 9?
4.Mention the factor pairs of 900.
5.What is the square of 900?
Important Glossaries for Factors of 900
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 900 are 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 900.
- 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 900 are (1, 900), (2, 450), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 900 is 2² × 3² × 5².
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find factors of 900 involves identifying pairs like (1, 900), (2, 450), etc.
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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.
