# Factors of 450

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

#### How to find factors of a number

 1.   Find factors of 450 using Division Method 2.   Find factors of 450 using Prime Factorization 3.   Find factors of 450 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 450

• Divide 450 by 1: 450 ÷ 1 : Remainder = 0
• Divide 450 by 2: 450 ÷ 2 : Remainder = 0
• Divide 450 by 3: 450 ÷ 3 : Remainder = 0
• Divide 450 by 5: 450 ÷ 5 : Remainder = 0
• Divide 450 by 6: 450 ÷ 6 : Remainder = 0
• Divide 450 by 9: 450 ÷ 9 : Remainder = 0
• Divide 450 by 10: 450 ÷ 10 : Remainder = 0
• Divide 450 by 15: 450 ÷ 15 : Remainder = 0
• Divide 450 by 18: 450 ÷ 18 : Remainder = 0
• Divide 450 by 25: 450 ÷ 25 : Remainder = 0
• Divide 450 by 30: 450 ÷ 30 : Remainder = 0
• Divide 450 by 45: 450 ÷ 45 : Remainder = 0
• Divide 450 by 50: 450 ÷ 50 : Remainder = 0
• Divide 450 by 75: 450 ÷ 75 : Remainder = 0
• Divide 450 by 90: 450 ÷ 90 : Remainder = 0
• Divide 450 by 150: 450 ÷ 150 : Remainder = 0
• Divide 450 by 225: 450 ÷ 225 : Remainder = 0
• Divide 450 by 450: 450 ÷ 450 : Remainder = 0

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

#### 2. Steps to find factors of 450 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 450 using the division method, follow these steps:

• Step 1. Start dividing 450 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 450, which is 2. Divide 450 by 2 to obtain the quotient (225).
450 ÷ 2 = 225
• Step 3. Repeat step 1 with the obtained quotient (225).
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 450 is, 450 = 2 x 3 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 450 as shown below:

So, the prime factorization of 450 is, 450 = 2 x 3 x 3 x 5 x 5.

#### 3. Find factors of 450 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 450 would be the two numbers which, when multiplied, give 450 as the result.

The following table represents the calculation of factors of 450 in pairs:

Factor Pair Pair Factorization
1 and 450 1 x 450 = 450
2 and 225 2 x 225 = 450
3 and 150 3 x 150 = 450
5 and 90 5 x 90 = 450
6 and 75 6 x 75 = 450
9 and 50 9 x 50 = 450
10 and 45 10 x 45 = 450
15 and 30 15 x 30 = 450
18 and 25 18 x 25 = 450

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 450. They are called negative pair factors.

Hence, the negative pairs of 450 would be ( -1 , -450 ) , ( -2 , -225 ) , ( -3 , -150 ) , ( -5 , -90 ) , ( -6 , -75 ) , ( -9 , -50 ) , ( -10 , -45 ) , ( -15 , -30 ) and ( -18 , -25 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 450 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 are exact divisors of 450.
• 1 is a factor of every number. Eg. 1 is a factor of 450.
• Every number is a factor of zero (0), since 450 x 0 = 0.

• Which is the smallest prime factor of 450?

Smallest prime factor of 450 is 2.

• Is 450 a perfect square?

No 450 is not a perfect square.

• What are five multiples of 450?

First five multiples of 450 are 900, 1350, 1800, 2250, 2700.

• What is prime factorization of 450?

Prime factorization of 450 is 2 x 3 x 3 x 5 x 5.

• What are factors of 450?

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

• How do you find factors of a negative number? ( eg. -450 )?

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

• Is 450 a whole number?

Yes 450 is a whole number.

• Which is greatest factor of 450?

The greatest factor of 450 is 225.

• What are the prime 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, 450.
Prime factors of 450 are 2, 3, 3, 5, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 450. Can you help her?

Prime factors of 450 are 2, 3, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 450?

Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.
Even factors of 450 are 2, 6, 10, 18, 30, 50, 90, 150, 450.
Hence, product of even factors of 450 is; 2 x 6 x 10 x 18 x 30 x 50 x 90 x 150 x 450 = 19683000000000.

Joy wants to calculate mean of all the factors of 450. Help him in finding the mean of 450.

Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 450 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 30 + 45 + 50 + 75 + 90 + 150 + 225 + 450 = 1209.
Hence, the mean of factors of 450 is 1209 ÷ 18 = 67.17.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 450? Help her in writing all the factors.

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

How many factors are there for 450?

Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.
So there are in total 18 factors.

Joey wants to write all the prime factors of 450 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 450 are 2, 3, 3, 5, 5.
So in exponential form it can be written as 2 x 32 x 52.

Kevin has been asked to write 17 factor(s) of 450. Can you predict the answer?

17 factor(s) of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225.