## Table of Contents

Factors are whole numbers that can be multiplied together to obtain another number. In other words, factors are the numbers that divide a given number evenly without leaving a remainder. When we find the factors of a number, we are identifying the numbers that, when multiplied, result in the original number.

These factors play an essential role in various mathematical operations, such as prime factorization, finding common multiples, simplifying fractions, and solving equations. Understanding factors is fundamental in mathematics and serves as a building block for many mathematical concepts and calculations.

## What are the Factors of 81?

Today, we are going to find out the factors by dividing 81 evenly, without leaving any remainder. The factors of 81 are 1, 3, 9, 27, and 81. You can find them by dividing 81 by different numbers and checking if the result is a whole number.

For example, 81 ÷ 3 = 27, so 3 and 27 are factors of 81. You can also use a factor tree to break down 81 into its prime factors, which are factors that cannot be divided further. Let’s find it out, follow each step

- Divide 81 by 1 = 81
- Divide 81 by 3 = 27
- Divide 81 by 9 = 9
- Divide 81 by 27 = 3
- Divide 81 by 81 = 1

Factors of 81 are 1, 3, 9, 27, and 81.

## Prime factors of 81

Prime factors of a number are the prime numbers that divide the given number exactly, without leaving a remainder. In other words, prime factors are the fundamental prime numbers that, when multiplied together, result in the original number.

The prime factors of 81 can be determined by dividing the number by prime numbers until it cannot be divided further.

For example, in the case of 81, we start by dividing it by 3, which is a prime number. Since 81 is divisible by 3, we obtain the quotient 27. Continuing the process, we divide 27 by 3 to get 9, and then divide 9 by 3 to get 3. Finally, we divide 3 by 3, resulting in 1. At this point, we have obtained all the prime factors of 81, which are 3, 3, 3, and 3.

The prime factors of 81 are 3, 3, 3, and 3. In exponential form, it can be written as 3^{4} = 81, indicating that 3 is raised to the power of 4.

## Factors of 81 in pairs

Do you want to know the pairs of factors of 81? The pairs of factors are the two numbers, when multiplied together, result in the original number.

We pick the pairs from factors, which are 1, 3, 9, 27, 81, and we will make two tables of it, 1st would be in positive numbers and 2nd would be in negative numbers.

### Positive pair

Multiplication | Positive Pair |
---|---|

1 × 81 = 81 | (1, 81) |

3 × 27 = 81 | (3, 27) |

9 × 9 = 81 | (9, 9) |

### Negative pair

Multiplication | Negative Pair |
---|---|

-1 × -81 = -81 | (-1, -81) |

-3 × -27 = -81 | (-3, -27) |

-9 × -9 = -81 | (-9, -9) |

## Solved factors of 81 with examples

**1. What are the factors of 81?**

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

**2. Is 81 a prime number?**

No, 81 is not a prime number because it has factors other than 1 and itself.

**3. How many factors does 81 have?**

81 has a total of 5 factors.

**4. What is the largest factor of 81?**

The largest factor of 81 is 81 itself.

**5. What are the prime factors of 81?**

The prime factorization of 81 is 3^4.

**6. Is 81 a perfect square?**

Yes, 81 is a perfect square because it can be expressed as 9^2.

**7. Can 81 be divided evenly by 7?**

No, 81 cannot be divided evenly by 7.

**8. What is the sum of the factors of 81?**

The sum of the factors of 81 is 121.

**9. What is the product of the factors of 81?**

The product of the factors of 81 is 177147.

**10. Can 81 be expressed as a product of prime numbers?**

Yes, the prime factorization of 81 is 3^4, where 3 is the only prime factor.