 # Factors of 450: Prime Factorization, Methods, and Examples

450 is an even composite number. In other words, there exist some integers whose product is 450. There is a total of 18 integers than can completely divide 450 which means 450 has 18 factors. The set of two factors that are multiplied to get 450 are called the factor pair of 450.

### Factors of 450

Here are the factors of number 450.

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

### Negative Factors of 450

The negative factors of 450 are similar to its positive aspects, just with a negative sign.

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

### Prime Factorization of 450

The prime factorization of 450 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3$^2$ x 5$^2$

In this article, we will learn about the factors of 450 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 450?

The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. These numbers are the factors as they do not leave any remainder when divided by 450.

The factors of 450 are classified as prime numbers and composite numbers. The prime factors of the number 450 can be determined using the prime factorization technique.

## How To Find the Factors of 450?

You can find the factors of 450 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 450, create a list containing the numbers that are exactly divisible by 450 with zero remainders. One important thing to note is that 1 and 450 are the 450’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 450 are determined as follows:

$\dfrac{450}{1} = 450$

$\dfrac{450}{2} = 225$

$\dfrac{450}{3} = 150$

$\dfrac{450}{5} = 90$

$\dfrac{450}{6} = 75$

$\dfrac{450}{9} = 50$

$\dfrac{450}{10} = 45$

$\dfrac{450}{15} = 30$

$\dfrac{450}{18} = 25$

$\dfrac{450}{25} = 18$

$\dfrac{450}{30} = 15$

$\dfrac{450}{45} = 10$

$\dfrac{450}{50} = 9$

$\dfrac{450}{75} = 6$

$\dfrac{450}{90} = 5$

$\dfrac{450}{150} = 3$

$\dfrac{450}{225} = 2$

$\dfrac{450}{450} = 1$

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

### Total Number of Factors of 450

For 450, there are 18 positive factors and 18 negative ones. So in total, there are 36 factors of 450.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of 450 is 1 x 2 x 3$^2$ x 5$^2$.

The exponent of 1 and 2 is 1 whereas the exponent of 3 and 5 is 2.

Adding 1 to each and multiplying them together results in 36.

Therefore, the total number of factors of 450 is 36. 18 are positive, and 18 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 450 by Prime Factorization

The number 450 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors. Before finding the factors of 450 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 450, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 450 can be expressed as:

450 = 2 x 3$^2$ x 5$^2$

## Factors of 450 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given. For 450, the factor pairs can be found as:

1 x 450 = 450

2 x 125 = 450

3 x 150 = 450

5 x 90 = 450

6 x 75 = 450

9 x 50 = 450

10 x 45 = 450

15 x 30 = 450

18x 25 = 450

The possible factor pairs of 450 are given as (1, 450), (2, 225), (3, 250), (5, 90), (6, 75) ,(9, 50), (10, 45), (15, 30), and (18, 25 ).

All these numbers in pairs, when multiplied, give 450 as the product.

The negative factor pairs of 450 are given as:

-1 x -450 = 450

-2 x -125 = 450

-3 x -150 = 450

-5 x -90 = 450

-6 x -75 = 450

-9 x -50 = 450

-10 x -45 = 450

-15 x -30 = 450

-18x -25 = 450

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -30, -45, -50, -75, -90, -150,- 225, and -450. are called negative factors of 450.

The list of all the factors of 450, including positive as well as negative numbers, is given below.

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

## Factors of 450 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 450 are there?

### Solution

The total number of Factors of 450 is 18.

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

### Example 2

Find the factors of 450 using prime factorization.

### Solution

The prime factorization of 450 is given as:

450 $\div$ 2 = 225

225 $\div$ 3 = 75

75 $\div$ 3 = 25

25 $\div$ 5 = 5

5 $\div$ 5 = 1

So the prime factorization of 450 can be written as:

2 x 3$^2$ x 5$^2$ = 450