Factors of 225
Did you know, 225 is an odd composite number which is a perfect square obtained by the product of 15 with itself? In this chapter, we will learn more about the factors of 225, prime factors of 225, and factors of 225 in pairs along with solved examples for a better understanding.
 Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, and 225
 Prime Factorization of 225: 225 = 3^{2} × 5^{2}
1.  What Are the Factors of 225? 
2.  How to Calculate the Factors of 225? 
3.  Factors of 225 by Prime Factorization 
4.  Factors of 225 in Pairs 
5.  FAQs on Factors of 225 
What Are the Factors of 225?
The factors of 225 are those numbers that completely divide it without leaving any remainder. So, when you multiply any two whole numbers with each other and get 225 as the answer, you can say that both these numbers are the factors of 225. Observe these numbers.
1 × 225 = 225
3 × 75 = 225
5 × 45 = 225
9 × 25 = 225
15 × 15 = 225
This can be continued until you reach 225 × 1 = 225. Thus, the factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
How to Calculate the Factors of 225?
Let's begin calculating the factors of 225, starting with the smallest whole number 1. Divide 225 with this number. Is the remainder 0?
Yes! So, we will get:
225/1 = 225
The next whole number is 3. Now divide 225 with this number.
225/3 = 75
3 × 75 = 225
Proceeding in a similar manner we get,
225 = 1 × 225
3 × 75 = 5 × 45 = 9 × 25 = 15 × 15
Did you notice anything special in the last line of the factors? We can see that the number 15 is repeating itself as a factor. So we know that 15 × 15 = 225.
In such cases, the number 225 is called a perfect square.
Hence, the factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Explore factors using illustrations and interactive examples.
 Factors of 625  The factors of 625 are 1, 5, 25, 125, 625
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 45  The factors of 45 are 1, 3, 5, 9, 15, 45
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25, 75
 Factors of 256  The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
 Factors of 441  The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441
Factors of 225 by Prime Factorization
Prime factorization means expressing a composite number as the product of its prime factors.
To get the prime factorization of 225, we divide it by its smallest prime factor, which is 3.
225/3 = 75
Now, 75 is divided by its smallest prime factor and the quotient is obtained.
This process goes on till we get the quotient as 1.
The prime factorization of 225 is shown below:
Observe the factor tree of 225 given below:
The prime factors of 225 are 5 × 5 × 3 × 3. This can also be written as is 5^{2} × 3^{2}.
Factors of 225 in Pairs
The pair of numbers which gives 225 when multiplied are known as factor pairs of 225. Observe the following factors of 225 in pairs.
Product form of 225  Pair factors 
1 × 225 = 225  1, 225 
3 × 75 = 225  3, 75 
5 × 45 = 225  5, 45 
9 × 25 = 225  9, 25 
15 × 15 = 225  15, 15 
But if we consider negative integers, then both the numbers in the pair factors should be negative. Since (  ve ×  ve) = +ve, the negative factor pairs of 225 can be listed as (1, 225), (3, 75), (5, 45), and so on.
Important Notes:
 As 225 ends with digit 5, it will have 5 as its factor. This holds true for all numbers that end with 5.
 All perfect square numbers have odd number of factors. Since 225 is a perfect square number, this applies here too. 225 has 9 factors in all.
Factors of 225 Solved Examples

Example 1: Peter and Andrew have rectangular carpets with dimensions 15 inches by 15 inches and 25 inches by 9 inches respectively. They place the two carpets one over another. Since the two of them do not overlap, Peter said that they don't have same area. However, Andrew does not agree with him.
Can you find out who is correct?
Solution:Area of a rectangle = length × breadth
For the first carpet,Area = 15 × 15 = 225
For the second carpet,Area = 25 × 9 = 225
This shows that their area is the same.
Did you notice that we indirectly used the different factors of 225 in order to prove the areas same? If pair factors of a number are multiplied to each other, they give the same product, the number itself!
Hence, the two carpets have equal area. 
Example 2: Jonathan needs to list the factors of 100 and 225 and then find the common factors between them. Can you help him?
Solution:
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.We can see that 1, 5, and 25 are the common factors among these.
Hence, the common factors are 1, 5, and 25.
FAQs on Factors of 225
What are the factors of 225?
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225
What are the prime factors of 225?
The prime factors of 225 are 3 and 5.
What is the prime factor decomposition of 225?
The prime factor decomposition of 225 is 3^{2} × 5^{2}.
Is 225 a prime number?
No, 225 has more than 2 factors. So it is not a prime number.
What are the common factors of 225, 450, and 600?
Factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
Factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 600 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The common factors of 225, 450, and 600 are 1, 3, 5, 15, 25, and 75.
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