Factors of 135
The number 135 can be represented in a unique form using its own digits in at least two ways as 135 = ( 1 + 3 + 5 )(1 × 3 × 5) and it can be written as the sum of consecutive power of its digits as 135 = 1^{1} + 3^{2} + 5^{3}. In this lesson, we will learn about the factors of 135, prime factors of 135, and factors of 135 in pairs along with solved examples for a better understanding.
 Factors of 135: 1, 3, 5, 9, 15, 27, 45 and 135
 Prime Factorization of 135: 135 = 3^{3} × 5
1.  What Are the Factors of 135? 
2.  How to Calculate Factors of 135? 
3.  Factors of 135 by Prime Factorization 
4.  Factors of 135 in Pairs 
5.  FAQs on Factors of 135 
What Are the Factors of 135?
Factors of 135 are numbers that exactly divide it and gives the remainder as 0. So, when you multiply any two whole numbers with each other and get 135 as the answer you can say that both of those two numbers will be the factors of 135. For example, you can get 135 as an answer as:
1 × 135 = 135
3 × 45 = 135
5 × 27 = 135
9 × 15 = 135
And so on can be continued until you reach 135 × 1 = 135. So in general we can say that the factors of 135 are all the integers that divide 135 without any remainder.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
How to Calculate the Factors of 135?
Let's begin calculating the factors of 135, starting with the smallest whole number, i.e., 1. Divide 135 with this number. Is the remainder 0?
Yes! So, we will get:
135/1 = 135
135 × 1 = 135
The next whole number is 3.
Now, divide 135 with this number.
135/3 = 45
45 × 3 = 135
Proceeding in a similar manner we get,
135 = 1 × 135 = 3 × 45 = 5 × 27 = 9 × 15
Hence, the factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
Explore factors using illustrations and interactive examples
 Factors of 125  The factors of 125 are 1, 5, 25, 125
 Factors of 225  The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 50, 75, 90, 225
 Factors of 144  The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
 Factors of 175  The factors of 175 are 1, 5, 7, 25, 35, 175
 Factors of 81  The factors of 81 are 1, 3, 9, 27, 81
 Factors of 45  The factors of 45 are 1, 3, 5, 9, 15, 45
Factors of 135 by Prime Factorization
Prime factorization means expressing a number as the product of its prime factors.
To get the prime factorization of 135, we divide it by its prime factor, say 3.
135/3 = 45
Now, 45 is divided by its prime factor and the quotient is obtained.
This process goes on till we get the quotient as 1.
45/3 = 15
Prime factorization of 135 can be shown as the below factor tree.
Prime factorization of 135 by upsidedown division is shown below:
The prime factorization of 135 is 3 × 3 × 3 × 5. Now that we have done the prime factorization of our number, we can multiply them and get the other factors.
Can you try and find out if all the factors are covered or not?
And as you might have already guessed it, for prime numbers, there are no other factors.
Factors of 135 in Pairs
The pair of numbers which gives 135 when multiplied is known as factor pairs of 135. The following are the factors of 135 in pairs.
Product form of 135 
Pair factor 
1 × 135 = 135 
1, 135 
3 × 45 = 135 
3, 45 
5 × 27 = 135 
5, 27 
9 × 15 = 135 
9, 15 
Pairs of factors of 135 are: (1, 135), (3, 45), (5, 27), and (9, 15).
Let's have a look at the negative pair factors of 135.
So, if we consider negative integers, then both the numbers in the pair factors will be negative.
It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.
So, we can have factor pairs of 135 as (1, 135), (3, 45), (5, 27), and (9, 15).
Important Notes:
 When you divide a number by its factor, the quotient of the division is also a factor.
 Factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
 135 is a nonperfect square number. Thus, it will have an even number of factors. This property holds for every nonperfect square number
Factors of 135 Solved Examples

Example 1: Jack needs to export 135 fountain pens and 100 ballpoint pens. He can pack only one type of pen in each box.
Also, he must pack the same number of pens in each box. What is the number of pens Jack can pack in each box?
Solution:
We are already familiar with the ways of finding factors.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.The factors that are common to both 100 and 135 are 1 and 5.
Hence, Jack can pack either 1 or 5 pens in a box. 
Example 2: Margot owns a bakery. She got an order of 135 cookies to be baked. If she bakes 3 cookies in an hour, how long will it take for her to bake all the cookies?
Solution:
Margot can bake 3 cookies in an hour.
The amount of time needed for Margot to bake 135 cookies will be given by:
135/3 = 45
Hence, Margot can bake 135 cookies in 45 hours.
FAQs on Factors of 135
What are all the factors of 135?
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
What are the odd factors of 135?
The odd factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
What are the prime factors of 135?
The prime factors of 135 are 3 and 5.
What are the pair factors of 135?
The pairs of factors of 135 are (1, 135), (3, 45), (5, 27), and (9, 15).
What are the common factors of 135 and 210?
Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The common factors of 135 and 210 are 1, 3, 5, and 15.
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