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 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.
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
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 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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and ways to avoid them.
There are 9 teams and 900 points. How will they divide the points equally?
They will get 100 points each.
To divide the points equally, we need to divide the total points by the number of teams.
900/9 = 100
A rectangular garden has a length of 30 meters and a total area of 900 square meters. Find the width.
30 meters.
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.
There are 18 baskets and 900 apples. How many apples will be in each basket?
Each basket will have 50 apples.
To find the apples in each basket, divide the total apples by the baskets.
900/18 = 50
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.
Dividing the participants by the total tables, we will get the number of participants at each table.
900/9 = 100
900 chairs need to be arranged in 10 rows. How many chairs will go in each row?
Each of the rows has 90 chairs.
Divide total chairs by rows.
900/10 = 90
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.