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Last updated on May 26th, 2025

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Factors of 450

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Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 450, how they are used in real life, and the tips to learn them quickly.

Factors of 450 for US Students
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What are the Factors of 450?

The numbers that divide 450 evenly are known as factors of 450.

 

A factor of 450 is a number that divides the number without remainder.

 

The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

 

Negative factors of 450: -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -30, -45, -50, -75, -90, -150, -225, and -450.

 

Prime factors of 450: 2, 3, and 5.

 

Prime factorization of 450: 2 × 3² × 5².

 

The sum of factors of 450: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 30 + 45 + 50 + 75 + 90 + 150 + 225 + 450 = 1488factors of 450

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How to Find Factors of 450?

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

 

  • Finding factors using multiplication
  • Finding factors using division method
  • Prime factors and Prime factorization
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 450. Identifying the numbers which are multiplied to get the number 450 is the multiplication method.

 

Step 1: Multiply 450 by 1, 450 × 1 = 450.

 

Step 2: Check for other numbers that give 450 after multiplying

2 × 225 = 450

3 × 150 = 450

5 × 90 = 450

6 × 75 = 450

9 × 50 = 450

10 × 45 = 450

15 × 30 = 450

18 × 25 = 450

 

Therefore, the positive factor pairs of 450 are: (1, 450), (2, 225), (3, 150), (5, 90), (6, 75), (9, 50), (10, 45), (15, 30), (18, 25).

 

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 450 by 1, 450 ÷ 1 = 450.

 

Step 2: Continue dividing 450 by the numbers until the remainder becomes 0.

450 ÷ 1 = 450

450 ÷ 2 = 225

450 ÷ 3 = 150

450 ÷ 5 = 90

450 ÷ 6 = 75

450 ÷ 9 = 50

450 ÷ 10 = 45

450 ÷ 15 = 30

450 ÷ 18 = 25

 

Therefore, the factors of 450 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.

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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
  • Using factor tree


Using Prime Factorization: In this process, prime factors of 450 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

 

The prime factors of 450 are 2, 3, and 5.

 

The prime factorization of 450 is: 2 × 3² × 5².

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Factor Tree

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

 

Step 1: Firstly, divide 450 by 2 to get 225.

 

Step 2: Now divide 225 by 3 to get 75.

 

Step 3: Then divide 75 by 3 to get 25.

 

Step 4: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.

 

So, the prime factorization of 450 is: 2 × 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 450: (1, 450), (2, 225), (3, 150), (5, 90), (6, 75), (9, 50), (10, 45), (15, 30), (18, 25).

 

Negative factor pairs of 450: (-1, -450), (-2, -225), (-3, -150), (-5, -90), (-6, -75), (-9, -50), (-10, -45), (-15, -30), (-18, -25).

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Common Mistakes and How to Avoid Them in Factors of 450

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

Mistake 1

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 450, 1 and 450 are also factors.

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Factors of 450 Examples

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Problem 1

There are 9 teams and 450 players. How will they divide the players equally?

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Each team will have 50 players.

Explanation

To divide the players equally, we need to divide the total players by the number of teams.
450/9 = 50

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Problem 2

A garden is rectangular, the length of the garden is 15 meters and the total area is 450 square meters. Find the width?

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30 meters.

Explanation

To find the width of the garden, we use the formula,
Area = length × width
450 = 15 × width
To find the value of width, we need to shift 15 to the left side.
450/15 = width

Width = 30.

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Problem 3

There are 18 baskets and 450 apples. How many apples will be in each basket?

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Each basket will have 25 apples.

Explanation

To find the apples in each basket, divide the total apples by the baskets.
450/18 = 25

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Problem 4

In a class, there are 450 students, and 15 groups. How many students are there in each group?

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There are 30 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.
450/15 = 30

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Problem 5

450 books need to be arranged on 9 shelves. How many books will go on each shelf?

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Each shelf has 50 books.

Explanation

Divide total books by shelves.
450/9 = 50

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FAQs on Factors of 450

1.What are the factors of 450?

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2.Mention the prime factors of 450.

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3.Is 450 a multiple of 9?

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4.Mention the factor pairs of 450?

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5.What is the square of 450?

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6.How can children in United States use numbers in everyday life to understand Factors of 450?

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7.What are some fun ways kids in United States can practice Factors of 450 with numbers?

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8.What role do numbers and Factors of 450 play in helping children in United States develop problem-solving skills?

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9.How can families in United States create number-rich environments to improve Factors of 450 skills?

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Important Glossaries for Factor of 450

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 450 are 1, 2, 3, 5, etc.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 450.
     
  • 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 450 are (1, 450), (2, 225), etc.
     
  • Prime factorization: Writing a number as a product of its prime factors. For example, 450 = 2 × 3² × 5².

  • Divisibility: A condition where one number can be divided by another without leaving a remainder. For example, 450 is divisible by 3.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they unlock a world full of possibilities! Our goal is to support kids throughout the United States in mastering key math skills, such as today’s Factors of 450, with a special emphasis on understanding factors—in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, tracking scores at a Little League baseball game, or budgeting their allowance to buy cool gadgets, understanding numbers builds their confidence for everyday tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in unique ways, we customize our methods to match each child’s style. From the busy streets of New York City to the sunny beaches of California, BrightChamps makes math come alive, bringing it closer to children everywhere. Let’s turn factors into an exciting part of every child’s math adventure!
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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.

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Fun Fact

: She loves to read number jokes and games.

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