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Factors of 900
With 900 being a perfect square, as well as one of the largest threedigit numbers in existence, it's has 27 pair factors inluding negative and positive both.
In this lesson, we will calculate the factors of 900, prime factors of 900, and factors of 900 in pairs along with solved examples for a better understanding.
 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 Factorization of 900 : 2^{2} × 3^{2} × 5^{2}
What are the Factors of 900?
A factor is a number that divides another number without leaving any remainder.
When we divide 900 by 3, the smallest odd prime number, it is exactly divisible and leaves no remainder.
Therefore 3 is a factor of 900.
Similarly, if we divide 900 by 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, and 450, it is completely divisible and leaves no remainder.
Therefore 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.
There are 27 factors of 900.
Note that 1 and the number are always factors of the number.
450 is the biggest factor of 900, excluding the number itself.
How to Calculate the Factors of 900?
The factors of 900 can be calculated using the division method.
In the division method, we find the numbers which divide 900 completely without leaving a remainder.
Factors of 900 by Division Method
For getting the factors of 900, it should be divided by natural numbers that exactly divide 900 and bring no remainder.
Likewise we have,
900 ÷ 1=900  900 ÷ 2=450 
900 ÷ 3=300  900 ÷ 4=225 
900 ÷ 5=180  900 ÷ 6=150 
900 ÷ 9=100  900 ÷ 20=45 
900 ÷ 25=36  900 ÷ 30=30 
900 ÷ 36=25  900 ÷ 45=220 
900 ÷ 50=18  900 ÷ 60=15 
900 ÷ 75=12  900 ÷ 90=10 
900 ÷ 100=9  900 ÷ 150=6 
900 ÷ 180=5  900 ÷ 225=4 
900 ÷ 300=3  900 ÷ 450=2 
Factors of 900 By Prime Factorization
Dividing a number by prime numbers is called the prime factorization method.
Then we express that number as a product of its prime factors.
We can find the prime factors by the division method or factor tree method.
Let us do prime factorization for 900.
Prime Factorization of 900 by Division Method
900 is divided by the smallest prime number which divides 900 exactly.
The quotient thus obtained is then divided by the smallest or second smallest prime number and the process continues till we get the quotient as 1.
Let us divide 900 by the prime number 2
900 ÷ 2 = 450
Here 450 is a composite number that can be further divided by 2
450 ÷ 2 = 225
Again 225 is a composite number that can be further divided by 3
225 ÷ 3 = 75
75 can be further divided by 3
75 ÷ 3 = 25
25 can be further divided by 5
25 ÷ 5 = 5
5 can be further divided by 5
5 ÷ 5 = 1
The division cannot continue further as we have the quotient as 1.
Therefore the prime factorization of 900 is 900=2 × 2 × 3 × 3 × 5 × 5 Or 2^{2} × 3^{2} × 5^{2}.
Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?
And as you might have already guessed, for prime numbers, there are no other factors.
Explore factors using illustrations and interactive examples
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 15  The factors of 15 are 1, 3, 5, 15
 Factors of 45  The factors of 45 are 1, 3, 5, 9, 15, 45
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
 Factors of 48  The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Challenging Question:
 If we know the factors of 90, it is easier to understand the factors of 900, 180, and other multiples of 90.
 If we need to check whether the given number is a factor of 900, divide the 900 by the given number and see if it completely divides 900 and leaves no remainder.
 900 can also have two negative numbers as pair factors, for example (30) x (30) = 900.
Factors of 900 in Pairs
Any set of two numbers which when multiplied give 900 as their product will be called pair factors of 900. Pair factors of 90 are:
180 × 5 = 900
300 × 3 = 900
450 × 2 = 900
900 × 1 = 900
225 × 4 = 900
150 × 6 = 900
10 × 90 = 900
12 × 75 = 900
18 × 50 = 900
15 × 60 = 900
20 × 45 = 900
25 × 36 = 900
30 × 30= 900
100 × 9 = 900
There are 27 factors 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).
Important Notes:
 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.
 There are 14 positive pair factors for 900.
 Prime factorization can be done by division method, factor tree method, and upside down division method.
Factors of 900 Solved Examples

Example 1:
Are all the numbers given below, the prime factors of 900?
2, 3, 5, 6, 9 and 10.Solution:
2, 3, and 5 are prime numbers because they cannot be further divided. 2, 3, and 5 divide 900 completely.
6, 9, and 10 can be further divided, they are composite numbers.
Therefore the prime factors of 900 among the given numbers are 2, 3, and 5 only. 
Example 2: James wants to find the prime factors of 900. Help him find the prime factors using factor tree.
Solution:
Prime factors of 900 using factor tree are:
FAQs on Factors of 900
What are the prime factors of 900?
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 of 900 are 1, 2, 3, and 5.
What are the factors of 900 in pairs?
(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).
What are all the positive factors of 900?
Positive 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.
What are all the negative pair factors 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).
How many factors of 900 are there?
There are 27 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.
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