# Factors of 225

Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225

#### How to find factors of a number

 1.   Find factors of 225 using Division Method 2.   Find factors of 225 using Prime Factorization 3.   Find factors of 225 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 225

• Divide 225 by 1: 225 ÷ 1 : Remainder = 0
• Divide 225 by 3: 225 ÷ 3 : Remainder = 0
• Divide 225 by 5: 225 ÷ 5 : Remainder = 0
• Divide 225 by 9: 225 ÷ 9 : Remainder = 0
• Divide 225 by 15: 225 ÷ 15 : Remainder = 0
• Divide 225 by 25: 225 ÷ 25 : Remainder = 0
• Divide 225 by 45: 225 ÷ 45 : Remainder = 0
• Divide 225 by 75: 225 ÷ 75 : Remainder = 0
• Divide 225 by 225: 225 ÷ 225 : Remainder = 0

Hence, Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225

#### 2. Steps to find factors of 225 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 225 using the division method, follow these steps:

• Step 1. Start dividing 225 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 225, which is 3. Divide 225 by 3 to obtain the quotient (75).
225 ÷ 3 = 75
• Step 3. Repeat step 1 with the obtained quotient (75).
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 225 is, 225 = 3 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 225 as shown below:

So, the prime factorization of 225 is, 225 = 3 x 3 x 5 x 5.

#### 3. Find factors of 225 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 225 would be the two numbers which, when multiplied, give 225 as the result.

The following table represents the calculation of factors of 225 in pairs:

Factor Pair Pair Factorization
1 and 225 1 x 225 = 225
3 and 75 3 x 75 = 225
5 and 45 5 x 45 = 225
9 and 25 9 x 25 = 225
15 and 15 15 x 15 = 225

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 225. They are called negative pair factors.

Hence, the negative pairs of 225 would be ( -1 , -225 ) , ( -3 , -75 ) , ( -5 , -45 ) , ( -9 , -25 ) and ( -15 , -15 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 25, 45, 75, 225 are exact divisors of 225.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 225 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 225.

• Which is the smallest prime factor of 225?

Smallest prime factor of 225 is 3.

• Is 225 a perfect square?

Yes 225 is a perfect square.

• What are five multiples of 225?

First five multiples of 225 are 450, 675, 900, 1125, 1350.

• What is prime factorization of 225?

Prime factorization of 225 is 3 x 3 x 5 x 5.

• What are factors of 225?

Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225.

• How do you find factors of a negative number? ( eg. -225 )?

Factors of -225 are -1, -3, -5, -9, -15, -25, -45, -75, -225.

• Is 225 a whole number?

Yes 225 is a whole number.

• Which is greatest factor of 225?

The greatest factor of 225 is 75.

• What are the prime factors of 225?

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225.
Prime factors of 225 are 3, 3, 5, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 225. Can you help her?

Prime factors of 225 are 3, 3, 5, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 225?

Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225.
Even factors of 225 are 0.
Hence, product of even factors of 225 is; 0 = 0.

Joy wants to calculate mean of all the factors of 225. Help him in finding the mean of 225.

Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 225 is 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 225 = 403.
Hence, the mean of factors of 225 is 403 ÷ 9 = 44.78.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 225? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 25, 45, 75, 225.
Negative factors are -1, -3, -5, -9, -15, -25, -45, -75, -225.

How many factors are there for 225?

Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225.
So there are in total 9 factors.

Joey wants to write all the prime factors of 225 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 225 are 3, 3, 5, 5.
So in exponential form it can be written as 32 x 52.

Kevin has been asked to write 8 factor(s) of 225. Can you predict the answer?

8 factor(s) of 225 are 1, 3, 5, 9, 15, 25, 45, 75.