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 = 1¹ + 3² + 5³. 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 = 3³ × 5

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 upside-down 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.

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 non-perfect square number. Thus, it will have an even number of factors. This property holds for every non-perfect square number

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.