Prime Factors of 729

Steps to find Prime Factors of 729 by 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.

Steps to find Prime Factors of 729 by 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.

What does Prime factor of a number mean?

A prime number in mathematics is defined as any natural number greater than 1, that is not divisible by any number except 1 and the number itself. When we express any number as the product of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 729 are 3 x 3 x 3 x 3 x 3 x 3.

Properties of Prime Factors

• Prime factors are the set of factors that are unique to the number given.
• 2 is the only even prime factor any number can have.
• Two prime factors are always coprime to each other.
• 1 is neither a prime number nor a composite number and also 1 is the factor of every given number. So, 1 is the factor of 729 but not a prime factor of 729.

Frequently Asked Questions

• Which is the smallest prime factor of 729?

  Smallest prime factor of 729 is 3.

• What is the prime factorization of 729?

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

• What is prime factorization of 729 in exponential form?

  Prime factorization of 729 in exponential form is 3⁶.

• Is 729 a prime number or a composite number?

  729 is a composite number.

• Is 729 a prime number?

  false, 729 is not a prime number.

• How to find prime factorization of 729 easily?

  To find prime factorization of 729 easily you can refer to the steps given on this page step by step.

• Which is the largest prime factors of 729?

  The largest prime factor of 729 is 3.

• What is the product of all prime factors of 729?

  Prime factors of 729 are 3 x 3 x 3 x 3 x 3 x 3. Therefore, their product is 729.

• What is the sum of all odd prime factors of 729?

  Prime factors of 729 are 3 , 3 , 3 , 3 , 3 , 3, out of which 3 , 3 , 3 , 3 , 3 , 3 are odd numbers. So, the sum of odd prime factors of 729 is 3 + 3 + 3 + 3 + 3 + 3 = 18.