 # Factors of 81

## Prime Factorization of 81

The Factors of 81 are all positive as well as the negative integers or whole numbers that you can evenly divide into the number 81 81. 81, when divided by a factor of 81, will equal to another factor of the number 81. Factor pairs of 81 are the whole numbers that can be either positive or negative but not in the form of a fraction or a decimal number. The factors of 81 and the prime factors of 81 are different since 81 is a composite number. Also, even though they are closely related, the prime factors of the number 81 and the prime factorization of the number 81 are not exactly the same. In this lesson, we will take a look at what are the factors of 81, the prime factorization of 81, the factor pairs of 81, and the prime factor tree of 81.

### What are the Factors of 81

Since all the factors of 81 are the numbers that you can evenly divide by the number 81, you simply need to divide this number 81 by all the numbers up to 81 and see which ones would result in an even quotient. When you do that, you will find that the following calculations resulted in the even quotient:

81 ÷ 1 = 81

81 ÷ 3 = 27

81 ÷ 9 = 9

81 ÷ 27 = 3

81 ÷ 81 = 1

The positive factors of the number 81 are therefore all the numbers that you used to divide above to and get an even number. Given below is the list of all the positive factors of 81 in the numerical order:

1, 3, 9, 27, 81.

The factors of 81 include all the negative numbers as well. Hence, all the positive factors of 81 can be easily converted to negative numbers. The list of the negative factors of the number 81 are:

-1, -3, -9, -27, -81.

### Factors of 81 in Pairs

The factors of 81 in pairs are all the combinations of two different factors which when multiplied together would equal to 81. Given below are all the positive factor pairs of 81.

1. 1 × 81 = 81

2. 3 × 27 = 81

3. 9 × 9 = 81

4. 27 × 3 = 81

5. 81 × 1 = 81

Since the factors of 81 include negative numbers as well, minus times minus equals to plus, and thus you can easily convert the positive factor pairs of the number 81 by putting a minus sign in front of all the factors and get all the negative factor pairs of 81.

1. -1 × -81 = 81

2. -3 × -27 = 81

3. -9 × -9 = 81

4. -27 × -3 = 81

5. -81 × -1 = 81

### Prime Factor Tree of 81

The prime factorization of 81 is given by 3 x 3 x 3 x 3. This is a different list of the prime factors and their multiplicities. Note that the prime factorization of the number 81 does not include the number 1, however, it does include every instance of the specific prime factor.

81 is the composite number. In contrast to the prime numbers that only have one factorization, the composite numbers like 81 have aa minimum of two factorizations.

To demonstrate what this means select the rightmost and the leftmost integer in 81, 27, 9, 3, 1, and then multiply these integers to get the number 81. This is called the first factorization.

Next, choose the second rightmost and the second leftmost number for obtaining the second factorization which also gives 81.

The prime factorization or the integer factorization of 81 means finding the set of the prime numbers that when multiplied together, would give you the original number 81. This is also referred to as the prime decomposition of 81.

Hence, the prime factors are written as 3 × 3 × 3 × 3 or $3^{4}$ in which 3 is the prime number.

1. How do you calculate the factors of 81?

Learn the following given steps to calculate the factors of 81.

1. The first step is to write the number 81.

Find the two numbers such that they give the result as 81 under the multiplication, say for example 3 and 27, since, 3 × 27 = 81.

As you know 3 is a prime number that has only two factors, that is 1 and the number itself. Hence, you cannot further factorize it.

3 = 3 × 1

2. Then look at the number 27, which is the composite number and not a prime number. Hence, it can be further factorized.

27 = 3 × 3 × 3 × 1

Hence, the factorization of 81 can be written as 81 = 3 x 3 × 3 × 3 × 1

3. Finally, write down all the numbers that you can obtain from the multiplication 3 × 3 × 3 × 3 × 1.

2. How to calculate the factors of 81 using the division method?

The number 81 is composite and it must have prime factors. Now let us find out how to calculate the prime factors of the number 81.

1. The first step is dividing the number 81 with the smallest prime factor, which is 3.

81 ÷ 3 = 27

2. Then again, divide the number 81 by 3 and the process will go on.

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

3. Finally, you will receive the number 1 at the end of this division process. Hence, you cannot proceed further.

Hence, the prime factors of 81 are written as 3 × 3 × 3 × 3 or 34, wherein 3 is the prime number.