Factors Of 81

Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second. For now let's just focus on the factors of 81, which are mentioned below:

Negative factors of 81: -1, -3, -9, -27, -81
Prime factors of 81: 3
Prime factorization of 81: 3⁴
The sum of factors of 81: 1 + 3 + 9 + 27 + 81= 121
 

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

• Use of Multiplication Method
• Use of Division Method
• Use of Prime Factors and Prime Factorization.

So, here we discuss a detailed explanation of the following methods:
 

In the multiplication method, we will try to find out the numbers that multiply together to give the value, 81. We will check the factors step by step:

Step 1: Start to multiply with numbers, which gives the value of 81.

Start with 1, and continue to multiply with other numbers. 

1 × 81 = 81
3 ×  27 = 81
9 ×  9  =  81 

Step 2: After the calculation, we get to these numbers, the factors of 81.

Step 3: The positive factor pairs of 81 found through multiplication are (1,81), (3,27), and (9,9)

Step 4: The negative factor pairs of 81 are (-1, -81), (-3, -27), and (-9, -9)
 

Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 81:

Step 1: Divide 81 by smaller numbers and see if there is any remainder. E.g., 81/1 = 81. 

Step 2: We will continue in the same way and check for other numbers as well. For 81, the factors are 1, 3, 9, 27, and 81 because 81 can be divided evenly by these numbers.
 

The prime factor of 81 is 3. The prime factors can be found using the methods given below:

• Prime Factorization
• Factor Tree

By Using Prime Factorization: It is a method in which we break down a number into its prime factor. 

3 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.

81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
 The prime factorization of 81 is :

 81 = 3⁴

With prime factorization, 81 can be broken down into prime factors 3.
 

A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.

Step 1: 81 divided by 3 gives us the quotient 27.

Step 2: Since 27 is not a prime number, it can be divided further.

The prime factorization of 81 is written below : 

81 = 3⁴
 

Every number has either a positive or negative factor. Let us look at those sets of factors.

Positive pair Factors:(1,81), (3,27), and (9,9)
Negative pair Factors: (-1,-81), (-3,-27), and (-9,-9)
 

• Factors:  Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.

• Prime Factors:  Prime factors of a number are a set of prime numbers that multiply together to give the original number. For 81, the prime factor is 3.

• Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).