# Factors of 135

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

#### How to find factors of a number

 1.   Find factors of 135 using Division Method 2.   Find factors of 135 using Prime Factorization 3.   Find factors of 135 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 135

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

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

#### 2. Steps to find factors of 135 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 135 using the division method, follow these steps:

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

So, the prime factorization of 135 is, 135 = 3 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 135 as shown below:

So, the prime factorization of 135 is, 135 = 3 x 3 x 3 x 5.

#### 3. Find factors of 135 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 135 would be the two numbers which, when multiplied, give 135 as the result.

The following table represents the calculation of factors of 135 in pairs:

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

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 135. They are called negative pair factors.

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

#### 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 number is a factor of zero (0), since 135 x 0 = 0.
• 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, 3, 5, 9, 15, 27, 45, 135 are exact divisors of 135.
• Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. Each factor divides 135 without leaving a remainder.

• Which is the smallest prime factor of 135?

Smallest prime factor of 135 is 3.

• Is 135 a perfect square?

No 135 is not a perfect square.

• What are five multiples of 135?

First five multiples of 135 are 270, 405, 540, 675, 810.

• What is prime factorization of 135?

Prime factorization of 135 is 3 x 3 x 3 x 5.

• What are factors of 135?

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

• How do you find factors of a negative number? ( eg. -135 )?

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

• Is 135 a whole number?

Yes 135 is a whole number.

• Which is greatest factor of 135?

The greatest factor of 135 is 45.

• What are the prime factors of 135?

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

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 135. Can you help her?

Prime factors of 135 are 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 135?

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

Joy wants to calculate mean of all the factors of 135. Help him in finding the mean of 135.

Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 135 is 1 + 3 + 5 + 9 + 15 + 27 + 45 + 135 = 240.
Hence, the mean of factors of 135 is 240 ÷ 8 = 30.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 135? Help her in writing all the factors.

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

How many factors are there for 135?

Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135.
So there are in total 8 factors.

Joey wants to write all the prime factors of 135 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 135 are 3, 3, 3, 5.
So in exponential form it can be written as 33 x 5.

Kevin has been asked to write 7 factor(s) of 135. Can you predict the answer?

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