Factors of 81: Methods and Facts

Factors of 81 are the list of numbers that can divide the original numeric figure into equal parts. In terms of understanding the factors of any numeric number, it is important to know about the factors.

• Factors are the numbers that can be multiplied together to get another number. 
• A numeric figure can have a lot of factors. 
• For example, 3 and 6 are the factors of 18, because 6 x 3 = 18.
• There is a list of numbers that can be factors of 81 and those can be positive as well as negative. Factors cannot be in decimals or fractions.

Read More: Cube and Cube Roots

Key Terms: Factors of 81, Whole Numbers, Pair Factors, Prime Factors, Prime Factorization, Division, Multiplication, Remainder

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What Can be the Factors of 81? 

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1, 3, 9, and 27 are the prime factors of 81. These numbers can divide into 81 properly and give the remainder as 0.

• Prime factors of 81: 3 × 3 × 3 × 3
• Negative factors of 81: -1,-3,-9,-27, and -81.
• Also, the possible factors of 81 are

81 ÷ 1 = 81

81 ÷ 9 = 9

81 ÷ 3 = 27

• Now, here are some examples to understand the pair factors properly.
• Factors of 18 = 1, 2, 3, 6, 9, and 18.
• Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
• Factors of 12 = 1, 2, 3, 4, 6, and 12.
• Factors of 14 = 1, 2, 7, and 14.

Read More: Factors of 24

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How to Calculate the Factors of 81?

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Various methods can be used to find out the factors of 81. For example, the division method and prime factorization can be used for the determination of factors of 81. For using the division method, one can consider the numbers that divide 81 without leaving any remainder. 

Read More: Factors of 72

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How to Find out the Factors of 81?

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Here are some simple steps to find out the factors of 81.

• First, write the number 81.
• Then, figure out two numbers that will give the result of 81 if those numbers get multiplied, such as 3 × 27=81
• So the number 3 can be considered as the prime factor which has only two factors (1 and 3). 
• It cannot be factorized further.
• The factorization of 81 is 81 = 3 x 3 × 3 × 3 × 1.
• Here it can be obtained that, the unique numbers are, 3 × 3 × 3 × 3 × 1.

Read More: Factors of 18

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Calculating the Factors of 81 Using the Division Method

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81 is a composite number and will have many factors. Here one will learn how to calculate the factors using the division method. First, one has to figure out the numbers which are starting from 1 and divide 81 without leaving any remainder.

• 81 ÷ 81 = 1
• 81 ÷ 9 = 9
• 81 ÷ 3 = 27
• 81 ÷ 1 = 81
• 81 ÷ 27 = 3

It shows the exact numbers are 1,3,9,27 and 81.

Read More: Types of Numbers

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Prime Factors of 81

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The composite number 81 has some prime factors. So, the first step is to divide 81 by the smallest prime number. For example, it can be 2.

• Then it will be 81 ÷ 2 = 40.5, and it can’t be a factor as it is a decimal number.
• Then, try to divide it using the next prime number which is 3. So the result will be 81 ÷ 3 = 27.
• Similarly, the process may go on,

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Finally, it can be stated that the prime factorization of 81 is 3 × 3 × 3 × 3 = 34. Here, 3 can be considered as the prime number and students can multiply it to find out other factors easily.

Read More: Quotient

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Some Important Facts

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A few important facts about factors of 81 are– 

• A factor of any number must be an exact divisor.
• No 1 is the common factor or the universal factor of every number.
• Any factor of any number can be equal to or less than the number. (3,9,27 are less than 81 and 81 itself is equal).
• The number itself is the highest factor.

Read More: Multiplication and Division of Integers

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Pair Factors of 81

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Pair factors of 81 can be both positive and negative. There are simplest ways to find out the pair factors of 81. Those are as follows,

• 3 × 27 = 81, (3, 27), pair factor of 81.

Likewise, other pair factors are,

• 1 × 81 = 81, then (1, 81), pair factor of 81
• 9 × 9 = 81, (9, 9), pair factor of 81.

Therefore, it can be observed that the positive pair factors are, (3, 27), (1, 81), and (9, 9).

However, the negative pair factors are,

• 3 × -27 = 81, (-3, -27) which can be considered as a pair factor of 81

Similarly, other pair factors are,

• -1 × -81 = 81, then (-1, - 81) which can be considered as a pair factor of 81
• -9 × -9 = 81, (-9, -9) which can be considered as a pair factor of 81.
• Thus, it can be stated that the negative pair factors of 81 are, (-3, -27), (-1, -81), and (-9, - 9).

Read More: Dividend

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Things to Remember

• The numbers that may be multiplied together to produce another number are known as factors. 
• Numerous variables can affect a numerical value.
• The factorization of 81 is 81 = 3 x 3 × 3 × 3 × 1.
• The prime factorization of 81 is 3 × 3 × 3 × 3 = 34.
• No 1 is the common factor or the universal factor of every number.
• Any factor of any number can be equal to or less than the number. (3,9,27 are less than 81 and 81 itself is equal).
• The number itself is the highest factor.