# Factors of 6561

Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, and 6561

#### How to find factors of a number

 1.   Find factors of 6561 using Division Method 2.   Find factors of 6561 using Prime Factorization 3.   Find factors of 6561 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 6561

• Divide 6561 by 1: 6561 ÷ 1 : Remainder = 0
• Divide 6561 by 3: 6561 ÷ 3 : Remainder = 0
• Divide 6561 by 9: 6561 ÷ 9 : Remainder = 0
• Divide 6561 by 27: 6561 ÷ 27 : Remainder = 0
• Divide 6561 by 81: 6561 ÷ 81 : Remainder = 0
• Divide 6561 by 243: 6561 ÷ 243 : Remainder = 0
• Divide 6561 by 729: 6561 ÷ 729 : Remainder = 0
• Divide 6561 by 2187: 6561 ÷ 2187 : Remainder = 0
• Divide 6561 by 6561: 6561 ÷ 6561 : Remainder = 0

Hence, Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, and 6561

#### 2. Steps to find factors of 6561 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 6561 using the division method, follow these steps:

• Step 1. Start dividing 6561 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 6561, which is 3. Divide 6561 by 3 to obtain the quotient (2187).
6561 ÷ 3 = 2187
• Step 3. Repeat step 1 with the obtained quotient (2187).
2187 ÷ 3 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 6561 is, 6561 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 6561 as shown below:

So, the prime factorization of 6561 is, 6561 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

#### 3. Find factors of 6561 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 6561 would be the two numbers which, when multiplied, give 6561 as the result.

The following table represents the calculation of factors of 6561 in pairs:

Factor Pair Pair Factorization
1 and 6561 1 x 6561 = 6561
3 and 2187 3 x 2187 = 6561
9 and 729 9 x 729 = 6561
27 and 243 27 x 243 = 6561
81 and 81 81 x 81 = 6561

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 6561. They are called negative pair factors.

Hence, the negative pairs of 6561 would be ( -1 , -6561 ) , ( -3 , -2187 ) , ( -9 , -729 ) , ( -27 , -243 ) and ( -81 , -81 ) .

#### 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, 243, 729, 2187, 6561 are exact divisors of 6561.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 6561 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 6561.

• Which is the smallest prime factor of 6561?

Smallest prime factor of 6561 is 3.

• Is 6561 a perfect square?

Yes 6561 is a perfect square.

• What are five multiples of 6561?

First five multiples of 6561 are 13122, 19683, 26244, 32805, 39366.

• What is prime factorization of 6561?

Prime factorization of 6561 is 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

• What are factors of 6561?

Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.

• How do you find factors of a negative number? ( eg. -6561 )?

Factors of -6561 are -1, -3, -9, -27, -81, -243, -729, -2187, -6561.

• Is 6561 a whole number?

Yes 6561 is a whole number.

• Which is greatest factor of 6561?

The greatest factor of 6561 is 2187.

• What are the prime factors of 6561?

The factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
Prime factors of 6561 are 3, 3, 3, 3, 3, 3, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 6561. Can you help her?

Prime factors of 6561 are 3, 3, 3, 3, 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 6561?

Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
Even factors of 6561 are 0.
Hence, product of even factors of 6561 is; 0 = 0.

Joy wants to calculate mean of all the factors of 6561. Help him in finding the mean of 6561.

Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 6561 is 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561 = 9841.
Hence, the mean of factors of 6561 is 9841 ÷ 9 = 1093.44.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 6561? Help her in writing all the factors.

Positive factors are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
Negative factors are -1, -3, -9, -27, -81, -243, -729, -2187, -6561.

How many factors are there for 6561?

Factors of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
So there are in total 9 factors.

Joey wants to write all the prime factors of 6561 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 6561 are 3, 3, 3, 3, 3, 3, 3, 3.
So in exponential form it can be written as 38.

Kevin has been asked to write 8 factor(s) of 6561. Can you predict the answer?

8 factor(s) of 6561 are 1, 3, 9, 27, 81, 243, 729, 2187.