# Factors of 729

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

#### How to find factors of a number

 1.   Find factors of 729 using Division Method 2.   Find factors of 729 using Prime Factorization 3.   Find factors of 729 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 729

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

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

#### 2. Steps to find factors of 729 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 729 using the division method, follow these steps:

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

So, the prime factorization of 729 is, 729 = 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 729 as shown below:

So, the prime factorization of 729 is, 729 = 3 x 3 x 3 x 3 x 3 x 3.

#### 3. Find factors of 729 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 729 would be the two numbers which, when multiplied, give 729 as the result.

The following table represents the calculation of factors of 729 in pairs:

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

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 729. They are called negative pair factors.

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

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 27, 81, 243, 729 are exact divisors of 729.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 729 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 729.

• Which is the smallest prime factor of 729?

Smallest prime factor of 729 is 3.

• Is 729 a perfect square?

Yes 729 is a perfect square.

• What are five multiples of 729?

First five multiples of 729 are 1458, 2187, 2916, 3645, 4374.

• What is prime factorization of 729?

Prime factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3.

• What are factors of 729?

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

• How do you find factors of a negative number? ( eg. -729 )?

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

• Is 729 a whole number?

Yes 729 is a whole number.

• Which is greatest factor of 729?

The greatest factor of 729 is 243.

• What are the prime factors of 729?

The factors of 729 are 1, 3, 9, 27, 81, 243, 729.
Prime factors of 729 are 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 729. Can you help her?

Prime factors of 729 are 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 729?

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

Joy wants to calculate mean of all the factors of 729. Help him in finding the mean of 729.

Factors of 729 are 1, 3, 9, 27, 81, 243, 729.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 729 is 1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093.
Hence, the mean of factors of 729 is 1093 ÷ 7 = 156.14.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 729? Help her in writing all the factors.

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

How many factors are there for 729?

Factors of 729 are 1, 3, 9, 27, 81, 243, 729.
So there are in total 7 factors.

Joey wants to write all the prime factors of 729 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 729 are 3, 3, 3, 3, 3, 3.
So in exponential form it can be written as 36.

Kevin has been asked to write 6 factor(s) of 729. Can you predict the answer?

6 factor(s) of 729 are 1, 3, 9, 27, 81, 243.