Factors of 225
2026-02-28 14:06 Diff
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Last updated on December 11, 2025

In mathematics, there are lots of numbers that when divided by other numbers leave no remainder, these numbers are called factors. We use it in our vehicles mileage and money handling. Now, we’ll learn what factors are and factors of 225 let us now see.

Factors Of 225

We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 225 has more than 2 factors. Let us find what the factors are.


Negative factors of 225:  -1, -3, -5, -9, -15, -25, -45, -75, and -225.


Prime factors of 225: The prime factors of 225 are 3 and 5.


Prime factorization of 225: 5×5×3×3.


The sum of factors of 225: 1+3+5+9+15+25+45+75+225= 403
 

How to find the factors of 225

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 225.

  • Multiplication Method
  • Division Method
  • Prime Factor and Prime Factorization
     

Finding The Factors Of 225 Using Multiplication

In the multiplication method, we find pairs of numbers where the product will be 225. In this process, possible steps will be - 


Step 1: Find all those numbers whose product will be 225.


Step 2: These numbers will be called the factors of 225.


Step 3: Students have to write these pairs of numbers for this method.


List of numbers whose product is 225


225×1= 225


75×3= 225


45×5= 225


25×9= 225


15×15= 225


So the pair of numbers whose product is 225 are (1,225), (3,75), (5,45), (9,25)  and (15,15).
 

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Finding Factors Using Division Method

For the division method, the process of division will go on until the remainder becomes zero.

Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 225÷1 = 225.


Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 225÷5= 45 and so on.


 

Prime Factors and Prime Factorization

Prime Factors Of 225: The prime factors of 225 are 5 and 7. We find the prime factors of 225 by two ways


Prime Factorization


Factor Tree


Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 225, the steps are like this:


225/5= 45


45/5= 9


9/3= 3


3/3= 1


As 3 is a prime number, it is only divisible by 3. Hence, The prime factorization of the number 225 is 5×5×3×3.
 

Factor Tree:

This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.


Step 1: 225 divided by 5 gives us the answer being 45.


Step 2: 45 divided by 5 gives us 9.


Step 3: 9 divided by 3 gives us 3.


Step 4: 3 divided by 3 gives us 1.


Step 5: This can’t be divided any further.

Factor Pairs

There are positive and negative factor pairs for a given number. Let us look at these factor pairs.


Positive Factor Pairs: (1,225), (3,75), (5,45), (9,25)  and (15,15).


Negative Factor Pairs: (-1,-225), (-3,-75), (-5,-45), (-9,-25)  and (-15,-15).
 

Common mistakes and how to avoid them in the factors of 225

It is very normal to make mistakes when learning to find the factors. Here are the commonly made mistakes by children. Avoid these when practicing!
 

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Problem 1

A plot of land is 225 square meters. If 15 families are to share the land equally, how much land will each family receive?

Okay, lets begin

 Each family gets 15 square meters of land.
 

Explanation

 225 square meters divided by 15 families means each family gets 15 square meters of land equally.

Well explained 👍

Problem 2

A shop sells boxes of chocolates, each containing 225 pieces. If a customer buys 9 boxes, how many chocolates does the customer buy in total?

Okay, lets begin

The customer buys 2025 chocolates in total.
 

Explanation

The customer buys 9 boxes, each with 225 chocolates. 225 multiplied by 9 equals 2025 chocolates.
 

Well explained 👍

Problem 3

A rectangle has an area of 225 square units. If one side is 25 units, what is the length of the other side?

Okay, lets begin

 The other side is 9 units long.

Explanation

 The area of a rectangle is length times width. So, 225 ÷ 25 = 9 units for the other side.
 

Well explained 👍

Problem 4

A farmer has 225 apples and wants to distribute them equally among 5 baskets. How many apples will each basket contain?

Okay, lets begin

Each basket will have 45 apples.
 

Explanation

 To share 225 apples equally, divide 225 by 5. This gives 45 apples in each basket.
 

Well explained 👍

Problem 5

A company packs items in boxes containing 225 units each. How many boxes are needed to pack 1800 items?

Okay, lets begin

 The company needs 8 boxes to pack 1800 items.
 

Explanation

 Divide 1800 items by 225 items per box, and you get 8 boxes needed to pack all items.
 

Well explained 👍

FAQs on Factors Of 225

1.How do we calculate the greatest factor of 225?

We have that the greatest factor of 225 is 225 because dividing it by itself equals 1, so that means that 225 itself is its largest factor.
 

2.What are the odd factors of 225?

All odd factors of 225 divided 225 evenly as they are: 1, 3, 5, 9, 15, 45, 75, and 225.
 

3.Is 225 a perfect square?

4.What is the square root of 225?

The square root of 225 is ±15. It’s the number that, when multiplied by itself, gives 225.
 

5.What are the multiples of 15 up to 225?

 The multiples of 15 up to 225 include 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, and 225.
 

Important Glossaries for Factors of 225

  • Prime Numbers: Numbers greater than 1 that have no positive divisors other than 1 and themselves. For example, 2, 3, 5, 7.
  • Square Root: A value that, when multiplied by itself, gives the original number. For example, the square root of 225 is ±15.
  • Sum of Factors: The total obtained by adding all the factors of a number. For 225, the sum of its factors is 403.
  • Remainder: The amount left over after division when one number does not divide the other evenly.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.