Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 9 teams and 450 players. How will they divide the players equally?
Each team will have 50 players.
To divide the players equally, we need to divide the total players by the number of teams.
450/9 = 50
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.
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.
There are 18 baskets and 450 apples. How many apples will be in each basket?
Each basket will have 25 apples.
To find the apples in each basket, divide the total apples by the baskets.
450/18 = 25
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.
Dividing the students by the total groups, we will get the number of students in each group.
450/15 = 30
450 books need to be arranged on 9 shelves. How many books will go on each shelf?
Each shelf has 50 books.
Divide total books by shelves.
450/9 = 50
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.
: She loves to read number jokes and games.