129 LearnersLast updated on May 26th, 2025
Factors of 450
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.
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 = 1488
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
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.
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.
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.
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).
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
Forgetting the number itself and 1 is a factor
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.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 450 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 450/1.5 = 300, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 450 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 450, but it has other factors like 10, 25.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 450 as 2 × 3² × 5² and missing all the key factors.
Factors of 450 Examples
Problem 1
There are 9 teams and 450 players. How will they divide the players equally?
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
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?
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.
Problem 3
There are 18 baskets and 450 apples. How many apples will be in each basket?
Each basket will have 25 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
450/18 = 25
Problem 4
In a class, there are 450 students, and 15 groups. How many students are there in each group?
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
Problem 5
450 books need to be arranged on 9 shelves. How many books will go on each shelf?
Each shelf has 50 books.
Explanation
Divide total books by shelves.
450/9 = 50
FAQs on Factors of 450
1.What are the factors of 450?
2.Mention the prime factors of 450.
3.Is 450 a multiple of 9?
4.Mention the factor pairs of 450?
5.What is the square of 450?
6.How can children in United States use numbers in everyday life to understand Factors of 450?
7.What are some fun ways kids in United States can practice Factors of 450 with numbers?
8.What role do numbers and Factors of 450 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 450 skills?
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.
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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
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