# Factors of 81

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

#### How to find factors of a number

 1.   Find factors of 81 using Division Method 2.   Find factors of 81 using Prime Factorization 3.   Find factors of 81 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 81

• Divide 81 by 1: 81 ÷ 1 : Remainder = 0
• Divide 81 by 3: 81 ÷ 3 : Remainder = 0
• Divide 81 by 9: 81 ÷ 9 : Remainder = 0
• Divide 81 by 27: 81 ÷ 27 : Remainder = 0
• Divide 81 by 81: 81 ÷ 81 : Remainder = 0

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

#### 2. Steps to find factors of 81 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 81 using the division method, follow these steps:

• Step 1. Start dividing 81 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 81, which is 3. Divide 81 by 3 to obtain the quotient (27).
81 ÷ 3 = 27
• Step 3. Repeat step 1 with the obtained quotient (27).
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 81 is, 81 = 3 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 81 as shown below:

So, the prime factorization of 81 is, 81 = 3 x 3 x 3 x 3.

#### 3. Find factors of 81 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 81 would be the two numbers which, when multiplied, give 81 as the result.

The following table represents the calculation of factors of 81 in pairs:

Factor Pair Pair Factorization
1 and 81 1 x 81 = 81
3 and 27 3 x 27 = 81
9 and 9 9 x 9 = 81

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 81. They are called negative pair factors.

Hence, the negative pairs of 81 would be ( -1 , -81 ) , ( -3 , -27 ) and ( -9 , -9 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 27, 81 are exact divisors of 81.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 81 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 81.

• Which is the smallest prime factor of 81?

Smallest prime factor of 81 is 3.

• Is 81 a perfect square?

Yes 81 is a perfect square.

• What are five multiples of 81?

First five multiples of 81 are 162, 243, 324, 405, 486.

• What is prime factorization of 81?

Prime factorization of 81 is 3 x 3 x 3 x 3.

• What are factors of 81?

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

• How do you find factors of a negative number? ( eg. -81 )?

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

• Is 81 a whole number?

Yes 81 is a whole number.

• Which is greatest factor of 81?

The greatest factor of 81 is 27.

• What are the prime factors of 81?

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

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 81. Can you help her?

Prime factors of 81 are 3, 3, 3, 3.
Hence, the product of prime factors of 3.

Can you help Rubel to find out the product of the even factors of 81?

Factors of 81 are 1, 3, 9, 27, 81.
Even factors of 81 are 0.
Hence, product of even factors of 81 is; 0 = 0.

Joy wants to calculate mean of all the factors of 81. Help him in finding the mean of 81.

Factors of 81 are 1, 3, 9, 27, 81.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 81 is 1 + 3 + 9 + 27 + 81 = 121.
Hence, the mean of factors of 81 is 121 ÷ 5 = 24.20.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 81? Help her in writing all the factors.

Positive factors are 1, 3, 9, 27, 81.
Negative factors are -1, -3, -9, -27, -81.

How many factors are there for 81?

Factors of 81 are 1, 3, 9, 27, 81.
So there are in total 5 factors.

Joey wants to write all the prime factors of 81 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 81 are 3, 3, 3, 3.
So in exponential form it can be written as 34.

Kevin has been asked to write 4 factor(s) of 81. Can you predict the answer?

4 factor(s) of 81 are 1, 3, 9, 27.