Factors of -225
2026-02-28 11:35 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-225

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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -225, how they are used in real life, and tips to learn them quickly.

What are the Factors of -225?

The numbers that divide -225 evenly are known as factors of -225.

A factor of -225 is a number that divides the number without remainder.

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

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

Prime factorization of -225: -1 × 3² × 5².

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

How to Find Factors of -225?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -225. Identifying the numbers which are multiplied to get the number -225 is the multiplication method.

Step 1: Multiply -225 by 1, -225 × 1 = -225.

Step 2: Check for other numbers that give -225 after multiplying

3 × -75 = -225

5 × -45 = -225

9 × -25 = -225

15 × -15 = -225

Therefore, the positive factor pairs of -225 are: (1, -225), (3, -75), (5, -45), (9, -25), (15, -15).

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method

Step 1: Divide -225 by 1, -225 ÷ 1 = -225.

Step 2: Continue dividing -225 by the numbers until the remainder becomes 0.

-225 ÷ 1 = -225

-225 ÷ 3 = -75

-225 ÷ 5 = -45

-225 ÷ 9 = -25

-225 ÷ 15 = -15

Therefore, the factors of -225 are: 1, 3, 5, 9, 15, 25, 45, 75, 225.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of -225 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

The prime factors of -225 are 3 and 5.

The prime factorization of -225 is: -1 × 3² × 5².

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 225 is divided by 3 to get 75.

Step 2: Now divide 75 by 3 to get 25.

Step 3: Then divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -225 is: -1 × 3² × 5².

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of -225: (1, -225), (3, -75), (5, -45), (9, -25), (15, -15).

Negative factor pairs of -225: (-1, 225), (-3, 75), (-5, 45), (-9, 25), (-15, 15).

Common Mistakes and How to Avoid Them in Factors of -225

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

Problem 1

There are 15 people and -225 apples. How will they distribute them equally?

Okay, lets begin

They will distribute -15 apples each.

Explanation

To divide the apples equally, we need to divide the total apples by the number of people.

-225/15 = -15

Well explained 👍

Problem 2

A rectangular garden has a length of 9 meters and a total area of 225 square meters. Find the width.

Okay, lets begin

25 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

225 = 9 × width

To find the value of width, we need to shift 9 to the left side.

225/9 = width

Width = 25.

Well explained 👍

Problem 3

There are 45 baskets and -225 oranges. How many oranges will be in each basket?

Okay, lets begin

Each basket will have -5 oranges.

Explanation

To find the oranges in each basket, divide the total oranges by the baskets.

-225/45 = -5

Well explained 👍

Problem 4

A school has a total of -225 students and wants to form 5 teams. How many students will be there in each team?

Okay, lets begin

There will be -45 students in each team.

Explanation

Dividing the students by the total teams, we will get the number of students in each team.

-225/5 = -45

Well explained 👍

Problem 5

225 chairs need to be arranged in 15 rows. How many chairs will go in each row?

Okay, lets begin

Each row will have 15 chairs.

Explanation

Divide total chairs by rows.

225/15 = 15

Well explained 👍

FAQs on Factors of -225

1.What are the factors of -225?

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

2.Mention the prime factors of -225.

The prime factors of -225 are -1 × 3² × 5².

3.Is -225 a multiple of 5?

4.Mention the factor pairs of -225?

(1, -225), (3, -75), (5, -45), (9, -25), and (15, -15) are the factor pairs of -225.

5.What is the square of 225?

Important Glossaries for Factors of -225

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
     
  • Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of -225.
     
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of -225 are (1, -225), (3, -75), etc.
     
  • Multiples: A multiple is a number that can be divided by another number without a remainder. For example, -225 is a multiple of 5.
     
  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of -225 is -1 × 3² × 5².

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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.