# Factors of 405

Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405

#### How to find factors of a number

 1.   Find factors of 405 using Division Method 2.   Find factors of 405 using Prime Factorization 3.   Find factors of 405 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 405

• Divide 405 by 1: 405 ÷ 1 : Remainder = 0
• Divide 405 by 3: 405 ÷ 3 : Remainder = 0
• Divide 405 by 5: 405 ÷ 5 : Remainder = 0
• Divide 405 by 9: 405 ÷ 9 : Remainder = 0
• Divide 405 by 15: 405 ÷ 15 : Remainder = 0
• Divide 405 by 27: 405 ÷ 27 : Remainder = 0
• Divide 405 by 45: 405 ÷ 45 : Remainder = 0
• Divide 405 by 81: 405 ÷ 81 : Remainder = 0
• Divide 405 by 135: 405 ÷ 135 : Remainder = 0
• Divide 405 by 405: 405 ÷ 405 : Remainder = 0

Hence, Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405

#### 2. Steps to find factors of 405 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 405 using the division method, follow these steps:

• Step 1. Start dividing 405 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 405, which is 3. Divide 405 by 3 to obtain the quotient (135).
405 ÷ 3 = 135
• Step 3. Repeat step 1 with the obtained quotient (135).
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 405 is, 405 = 3 x 3 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 405 as shown below:

So, the prime factorization of 405 is, 405 = 3 x 3 x 3 x 3 x 5.

#### 3. Find factors of 405 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 405 would be the two numbers which, when multiplied, give 405 as the result.

The following table represents the calculation of factors of 405 in pairs:

Factor Pair Pair Factorization
1 and 405 1 x 405 = 405
3 and 135 3 x 135 = 405
5 and 81 5 x 81 = 405
9 and 45 9 x 45 = 405
15 and 27 15 x 27 = 405

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 405. They are called negative pair factors.

Hence, the negative pairs of 405 would be ( -1 , -405 ) , ( -3 , -135 ) , ( -5 , -81 ) , ( -9 , -45 ) and ( -15 , -27 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 27, 45, 81, 135, 405 are exact divisors of 405.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 405 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 405.

• Which is the smallest prime factor of 405?

Smallest prime factor of 405 is 3.

• Is 405 a perfect square?

No 405 is not a perfect square.

• What are five multiples of 405?

First five multiples of 405 are 810, 1215, 1620, 2025, 2430.

• What is prime factorization of 405?

Prime factorization of 405 is 3 x 3 x 3 x 3 x 5.

• What are factors of 405?

Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.

• How do you find factors of a negative number? ( eg. -405 )?

Factors of -405 are -1, -3, -5, -9, -15, -27, -45, -81, -135, -405.

• Is 405 a whole number?

Yes 405 is a whole number.

• Which is greatest factor of 405?

The greatest factor of 405 is 135.

• What are the prime factors of 405?

The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
Prime factors of 405 are 3, 3, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 405. Can you help her?

Prime factors of 405 are 3, 3, 3, 3, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 405?

Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
Even factors of 405 are 0.
Hence, product of even factors of 405 is; 0 = 0.

Joy wants to calculate mean of all the factors of 405. Help him in finding the mean of 405.

Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 405 is 1 + 3 + 5 + 9 + 15 + 27 + 45 + 81 + 135 + 405 = 726.
Hence, the mean of factors of 405 is 726 ÷ 10 = 72.60.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 405? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
Negative factors are -1, -3, -5, -9, -15, -27, -45, -81, -135, -405.

How many factors are there for 405?

Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
So there are in total 10 factors.

Joey wants to write all the prime factors of 405 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 405 are 3, 3, 3, 3, 5.
So in exponential form it can be written as 34 x 5.

Kevin has been asked to write 9 factor(s) of 405. Can you predict the answer?

9 factor(s) of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135.