Factors of 81 Using Prime Factorization
What are the Factors of 81?
The factors of 81 are those natural numbers that divide 81 without leaving any remainder. In other words, we can say that the factors of 81 will divide it evenly.
The factors of 81 can be positive as well as negative, but they cannot be decimal numbers or fractions. The quotient obtained on dividing 81 by its factor is also a factor of 81.
The Factors of 81?
Factors | Factors pairs | Prime factorization |
|---|---|---|
1, 3, 9, 27, 81 | (1, 81), (3, 27), (9, 9) | 81 = 3 \( \times \) 3 \( \times \) 3 \( \times \) 3 |
For example, 3 is a factor of 81 because on dividing 81 by 3, we get no remainder and 27, that is, the quotient in this division, which is also a factor of 81.
[Note: When a number is divided by its factor, the quotient obtained is also a factor of the original number.]
Factor list for the Number 81
Divisor | Is the number a factor of 81? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 \( \times \) 81 = 81 |
2 | No, 81 is odd | - |
3 | Yes, 8 + 1 = 9 is divisible by 3 | 3 \( \times \) 27 = 81 |
4 | No, 81 \( \div \) 4 = 20 R1 | - |
5 | No, ones digit is not 0 or 5 | - |
6 | No, 81 \( \div \) 6 = 13 R3 | - |
7 | No, 81 \( \div \) 7 = 11 R4 | -- |
8 | No, 81 \( \div \) 8 = 10 R1 | |
9 | Yes, 81 \( \div \) 9 = 9 R0 | 9 \( \times \) 9 = 81 |
We can stop after checking for 9 because the factor pairs start to repeat after 9.
So the factors of 81 are 1, 3, 9, 27, and 81.
The Prime Factors of 81
A factor tree can be used to determine the prime factors of 81, as shown in the image.
From the factor tree, we can observe that the prime factorization of 81 is: 3 \( \times \) 3 \( \times \) 3 \( \times \) 3 = 3\( ^4 \)
This means 3 is the only prime factor of 81.
The Factor Pairs of 81
The factor pair of any number is a set of two of its factors, which when multiplied, results in that number as the product. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 81 is a set of two factors of 81, which when multiplied give 81 as the product.
Thus, the factor pairs of 81 can be obtained from the list of its factors.
Positive factors of 81 | Positive factor pairs of 81 |
|---|---|
1 \( \times \) 81 | (1, 81) |
3 \( \times \) 27 | (3, 27) |
9 \( \times \) 9 | (9, 9) |
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Rapid Recall
What are the factors of 81?
Solved Factors on 81 Examples
Example 1: 81 strawberries are distributed evenly between a group of 9 children. Can each child get an equal number of strawberries? How many strawberries will each child get?
Solution:
Number of children = 9
Number of strawberries = 81
Since 9 is a factor of 81, the strawberries can be divided into equal shares without cutting them into smaller pieces.
Dividing 81 by 9:
81 \( \div \) 9 = 9
Hence, the strawberries can be distributed equally among the 9 children. Also, each child will get 9 strawberries.
Example 2: What are the common factors of 81 and 18?
Solution:
The factors of 81 are 1, 3, 9, 27, and 81
The factors of 18 are 1, 2, 3, 6, 9, and 18.
So, the common factors of 81 and 18 are 1, 3, and 9.
Example 3: Find the greatest common factor of 81 and 72.
Solution:
The factors of 81 are 1, 3, 9, 27, and 81
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
So, the common factors of 81 and 72 are 1, 3, and 9.
Therefore, the greatest common factor of 81 and 72 is 9.
The prime factorisation of 81 is 3\( ^4 \).
So, the prime factor of 81 is 3.
Yes, 81 is a composite number as it has factors other than 1 and itself, that is, 81. In other words, the number 81 has more than two factors. Its factors are 3, 9, and 27, other than 1 and 81.
The factors of 81 are 1, 3, 9, 27, and 81.
So, the smallest factor of 81 is 1, and the greatest factor is 81 itself.
The factors of 81 are 1, 3, 9, 27, and 81.
The sum of all the factors of 81 is
= 1 + 3 + 9 + 27 + 81 = 121
Hence, the sum is 121.
When 81 is divided by 10, the remainder is 1, that is, not zero. Hence, 10 is not a factor of 81.