Answer:
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: 34 or 3 × 3 × 3 × 3
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 upside-down division method as:
Thus, the prime factorization is 3 × 3 × 3 × 3 = 34. Now that we have completed the prime factorization of the number, we can multiply them and get the other factors.
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).
