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 = 3² × 5²

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 5² × 3².

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.

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.

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 3² × 5².

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.