Factors of 900

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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

How to find factors of a number

1. Steps to find factors of 900 using Division Method

Find all the numbers which can divide 900 without leaving any remainder, starting from number 1 upto 450 (half of 900). The number 1 and the number (900) itself are always factors of the given number (900).
Note down all such number. All of those numbers are factors of 900.

Example: Find factors of 900

Divide 900 by 1: 900 ÷ 1 : Remainder = 0
Divide 900 by 2: 900 ÷ 2 : Remainder = 0
Divide 900 by 3: 900 ÷ 3 : Remainder = 0
Divide 900 by 4: 900 ÷ 4 : Remainder = 0
Divide 900 by 5: 900 ÷ 5 : Remainder = 0
Divide 900 by 6: 900 ÷ 6 : Remainder = 0
Divide 900 by 9: 900 ÷ 9 : Remainder = 0
Divide 900 by 10: 900 ÷ 10 : Remainder = 0
Divide 900 by 12: 900 ÷ 12 : Remainder = 0
Divide 900 by 15: 900 ÷ 15 : Remainder = 0
Divide 900 by 18: 900 ÷ 18 : Remainder = 0
Divide 900 by 20: 900 ÷ 20 : Remainder = 0
Divide 900 by 25: 900 ÷ 25 : Remainder = 0
Divide 900 by 30: 900 ÷ 30 : Remainder = 0
Divide 900 by 36: 900 ÷ 36 : Remainder = 0
Divide 900 by 45: 900 ÷ 45 : Remainder = 0
Divide 900 by 50: 900 ÷ 50 : Remainder = 0
Divide 900 by 60: 900 ÷ 60 : Remainder = 0
Divide 900 by 75: 900 ÷ 75 : Remainder = 0
Divide 900 by 90: 900 ÷ 90 : Remainder = 0
Divide 900 by 100: 900 ÷ 100 : Remainder = 0
Divide 900 by 150: 900 ÷ 150 : Remainder = 0
Divide 900 by 180: 900 ÷ 180 : Remainder = 0
Divide 900 by 225: 900 ÷ 225 : Remainder = 0
Divide 900 by 300: 900 ÷ 300 : Remainder = 0
Divide 900 by 450: 900 ÷ 450 : Remainder = 0
Divide 900 by 900: 900 ÷ 900 : Remainder = 0

Hence, 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

2. Steps to find factors of 900 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 900 using the division method, follow these steps:

Step 1. Start dividing 900 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
Step 2. After finding the smallest prime factor of the number 900, which is 2. Divide 900 by 2 to obtain the quotient (450).
900 ÷ 2 = 450
Step 3. Repeat step 1 with the obtained quotient (450).
450 ÷ 2 = 225

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

So, the prime factorization of 900 is, 900 = 2 x 2 x 3 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 900 as shown below:

So, the prime factorization of 900 is, 900 = 2 x 2 x 3 x 3 x 5 x 5.

3. Find factors of 900 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 900 would be the two numbers which, when multiplied, give 900 as the result.

The following table represents the calculation of factors of 900 in pairs:

Factor Pair	Pair Factorization
1 and 900	1 x 900 = 900
2 and 450	2 x 450 = 900
3 and 300	3 x 300 = 900
4 and 225	4 x 225 = 900
5 and 180	5 x 180 = 900
6 and 150	6 x 150 = 900
9 and 100	9 x 100 = 900
10 and 90	10 x 90 = 900
12 and 75	12 x 75 = 900
15 and 60	15 x 60 = 900
18 and 50	18 x 50 = 900
20 and 45	20 x 45 = 900
25 and 36	25 x 36 = 900
30 and 30	30 x 30 = 900

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 900. They are called negative pair factors.

Hence, the negative pairs of 900 would be ( -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 factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

Each number is a factor of itself. Eg. 900 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 900.
Every number is a factor of zero (0), since 900 x 0 = 0.
Every number other than 1 has at least two factors, namely the number itself and 1.
Every factor of a number is an exact divisor of that number, example 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 are exact divisors 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, 900. Each factor divides 900 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 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 are all less than or equal to 900.

Frequently Asked Questions

Which is the smallest prime factor of 900?
Smallest prime factor of 900 is 2.
Is 900 a perfect square?
Yes 900 is a perfect square.
What are five multiples of 900?
First five multiples of 900 are 1800, 2700, 3600, 4500, 5400.
What is prime factorization of 900?
Prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5.
What are 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, 900.
How do you find factors of a negative number? ( eg. -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, -900.
Is 900 a whole number?
Yes 900 is a whole number.
Which is greatest factor of 900?
The greatest factor of 900 is 450.
What are the prime factors of 900?
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, 900.
Prime factors of 900 are 2, 2, 3, 3, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 900. Can you help her?

Prime factors of 900 are 2, 2, 3, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even 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, 900.
Even factors of 900 are 2, 4, 6, 10, 12, 18, 20, 30, 36, 50, 60, 90, 100, 150, 180, 300, 450, 900.
Hence, product of even factors of 900 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 30 x 36 x 50 x 60 x 90 x 100 x 150 x 180 x 300 x 450 x 900 = 1.9835929036800002e+29.

Joy wants to calculate mean of all the factors of 900. Help him in finding the mean 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, 900.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 900 is 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 = 2821.
Hence, the mean of factors of 900 is 2821 ÷ 27 = 104.48.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 900? Help her in writing all the factors.

Positive factors 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, 900.
Negative factors 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, -900.

How many factors are there for 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, 900.
So there are in total 27 factors.

Joey wants to write all the prime factors of 900 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 900 are 2, 2, 3, 3, 5, 5.
So in exponential form it can be written as 2² x 3² x 5².

Kevin has been asked to write 26 factor(s) of 900. Can you predict the answer?

26 factor(s) 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.