Factors of 81

The factors of 81 are the numbers that divide the original number into equal parts. Factors of 81, when multiplied in pair, results in the actual number. Factor pairs of 81 are the integers which could be either positive or negative but not a fraction or decimal number. For example, 1 and 81 make the pair factors of 81 such that 1 multiplied by 81 equals to 81. In the same way, we can take negative values of 1 and 81 such that their product results in 81 itself,  (-1 x -81 = 81).

To find the factors of a number, we can use the factorisation method. In the factorization method, first, consider the numbers 1 and 81 as factors and continue finding the other pair of factors of 81, giving the results an original number. To understand this method better, read the article below to find the factors of 81 in pairs. Also, the prime factors with the help of the division method is explained below.

What are the Factors of 81?

The factors of 81 are 1, 3, 9, 27 and 81. Each of the factors of 81 divides 81 evenly.

Pair Factors of 81

To find the factors of 81 in pairs, multiply the two numbers in a pair to get the original number as 81; such numbers are as follows

If 1 × 81 = 81, then (1, 81) is a pair factor of 81.

Similarly, let us find other pair factors.

3 × 27 = 81, (3, 27) is a pair factor of 81

9 × 9 = 81, (9, 9) is a pair factor of 81

Therefore, the positive pair factors are (1, 81), (3, 27), and (9, 9).

To find the negative pair factors, proceed with the following steps

If -1 × -81 = 81, then (-1,- 81) is a pair factor of 81

-3 × -27 = 81, (-3, -27) is a pair factor of 81

-9 × -9 = 81, (-9, -9) is a pair factor of 81.

Therefore, the negative pair factors are (-1, -81), (-3, -27), and (-9,- 9).

How to Find the Factors of 81?

Go through the following steps to calculate the factors.

• First, write the number 81
• Find the two numbers, which give the result as 81 under the multiplication, say 3 and 27, such as 3 × 27 = 81.
• We know that 3 is a prime number which has only two factors, i.e., 1 and the number itself( 1 and 3). So, it cannot be further factorized.
  3 = 3 × 1
• Look at the number 27, which is a composite number but not a prime number. So it can be further factorized.
  27 = 3 × 3 × 3 × 1
• Therefore, the factorization of 81 is written as 81 = 3 x 3 × 3 × 3 × 1
• Finally, write down all the unique numbers which we can obtain from 3 × 3 × 3 × 3 × 1.

Prime Factors of 81

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

• The first step is to divide the number 81 with the smallest prime number say 2.
  81 ÷ 2 = 40.5, not a factor since it is a decimal number
• Now, divide 81 by the next prime number, say 3.

81 ÷ 3 = 27

Again, divide 81 by 3 and the process goes on.

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

• Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors are written as 3 × 3 × 3 × 3 or 3⁴, where 3 is a prime number.

Important Facts of Factors of 81

• A factor of any number is its exact divisor (1, 3, 9, 27 and 81 divides 81 exactly)
• 1 is a factor of every number
• Any factor of a number is always less than or equal to the number itself (1, 3, 9, 27, 81 are less than or equal to 81)
• The number itself is the greatest factor. (81 is the greatest factor of itself)

Video Lesson on Prime Factors

Solved Examples on Factors of 81

Q.1: There are 81 chocolates to be distributed among 9 students. How many chocolates will each student get?

Solution: Given,

Number of chocolates = 81

Number of students = 9

Number of chocolates for each student = 81/9 = 9

Hence, each student will get 9 chocolates.

Q.2: What are the common factors of 81 and 61?

Solution: The factors of 81 are 1, 3, 9, 27 and 81.

61 is a prime number, thus it has only two factors, 1 and 61.

Hence the common factor of 81 and 61 is 1.

Stay tuned with BYJU’S to know more about factors and prime factors of other numbers and also download BYJU’S – The Learning App for a better experience and clarification.