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Factors of 81
Factors of 81 are the list of numbers that can divide 81 into equal parts. The factors of 81 can be both positive as well as negative. 81 is a perfect square number. Hence, we can express it as 9 × 9 = 81. 9 can further be factored as 3 × 3 = 9. In this lesson, we will learn about the prime factors of 81, its pair factors, and its prime factorization. We will end this lesson by solving some examples for better understanding.
 Factors of 81: 1, 3, 9, 27, 81
 Negative Factors of 81: 1, 3, 9, 27 and 81
 Prime Factorization of 81: 3^{4} or 3 × 3 × 3 × 3
1.  What are Factors of 81? 
2.  How to Calculate Factors of 81? 
3.  Factors of 81 by Prime Factorization 
4.  Factors of 81 in Pairs 
5.  Important Notes 
6.  FAQs on Factors of 81 
7.  Thinking Out of the Box! 
What are Factors of 81?
Factors of 81 are those numbers that divide it completely and give the remainder as 0. Thus, the possible factors of 81 are:
 81 ÷ 1 = 81
 81 ÷ 3 = 27
 81 ÷ 9 = 9
Explore factors using illustrations and interactive examples
 Factors of 16: The factors of 16 are 1, 2, 4, 8 and 16.
 Factors of 15: The factors of 15 are 1 , 3, 5 and 15.
 Factors of 75: The factors of 75 are 1, 3, 5, 15, 25 and 75
 Factors of 90: The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
 Factors of 9: The factors of 9 are 1, 3 and 9.
How to Calculate the Factors of 81?
We can use different methods to find the factors of 81 such as the division method and prime factorization. In division method, we observe the numbers that divide 81 exactly without leaving a remainder and in prime factorization, we express 81 as a product of its prime factors.
Factors of 81 by Division Method
The number 81 is a composite number; hence, it will have many factors. Now let us learn how to calculate the factors of the number 81. Find the numbers starting from 1 that divide 81 exactly without leaving a remainder.
 81 ÷ 1 = 81
 81 ÷ 3 = 27
 81 ÷ 9 = 9
 81 ÷ 27 = 3
 81 ÷ 81 = 1
The division shows that the number 81 is exactly divisible by 1, 3, 9, 27, and 81.
Factors of 81 by Prime Factorization
 Method 1: The factors of 81 can be represented by the factor tree method as:
 Method 2: The factors of 81 can be represented by the upsidedown division method as:
Thus, the prime factorization is 3 × 3 × 3 × 3 = 3^{4}. Now that we have completed the prime factorization of the number, we can multiply them and get the other factors.
Factors of 81 in Pairs
Product form of 81  Factors of 81 in pairs 
1 × 81 = 81  (1, 81) 
3 × 27 = 81  (3, 27) 
9 × 9 = 81  (9, 9) 
Important Notes:
 The numbers which we multiply to get 81 are the factors of 81.
 Factors of 81 are 1, 3, 9, 27, and 81.
 1 is a universal factor. It is a factor of all numbers. The number itself is a factor of the number as it divides itself exactly.
 Factors of 81 in pairs are (1, 81), (3, 27), and (9, 9).
Think Tank
 Can you think of the negative factors of 81?
 Can multiples of 81 also be factors of 81?
Factors of 81 Solved Examples

Example 1: What are the negative pair factors of 81?
Solution:
1 × 81 = 81 and hence, (1, 81) is a pair factor of 81.
3 × 27 = 81 and hence, (3, 27) is a pair factor of 81.
9 × 9 = 81, and hence, (9, 9) is a pair factor of 81.
Therefore, the negative pair factors are (1, 81), (3, 27), and (9, 9).

Example 2: List the prime factors of 81.
Solution:
The number 81 is a composite number. To calculate the prime factors of 81, we will use the divisibility tests. We know that 81 is an odd number. Hence, we proceed to check the divisibility by 3.
81 ÷ 3 = 27
27 ÷ 3 = 9,
9 ÷ 3 = 3.
3 ÷ 3 = 1
Thus, we get the prime factorization of 81 = 3 × 3 × 3 × 3 which means that the only prime factor is 3.
FAQs on Factors of 81
What are the Factors of 81?
There are 5 factors of 81. They are 1, 3, 9, 27, and 8.
Is 81 a Prime number or a Composite number?
 A prime number does not have a factor other than 1 and itself.
 A composite number has factors other than 1 and itself.
 Factors of 81 are 1, 3, 9, 27, and 81. Hence, it is a composite number.
What are the Common Factors of 81 and 9?
Factors of 81 are 1, 3, 9, 27, and 81 and the factors of 9 are 1, 3 and 9. Therefore, the common factors of 81 and 9 are 1, 3 and 9.
What are the Positive and Negative Factors of 81?
The positive factors of 81 are 1, 3, 9, 27, and 81. The negative factors of 81 are 1, 3, 9, 27, and 81.
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