Prime Factors of 729

Looking to get a list of the prime factors of 729? In this article we'll give you all of the information you need, including the definition of the prime factors of 729, how to calculate the prime factors of 729 (also known as the prime factorization of 729). As a bonus, we'll also list out the prime factor tree of 729 the product of prime factors of 729, and tell you how many prime factors 729 has.

Prime Factors of 729 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 729, we're talking about the building blocks of the number. A prime factor is a positive integer that can only be divided by 1 and itself. The prime factors of 729 are all of the prime numbers in it that when multipled together will equal 729.

Let's look at how to find all of the prime factors of 729 and list them out.

How to Find the Prime Factors of 729

You'll often see the process of finding prime factors of 729 referred to as prime factorization. To get the prime factors of 729 we need to divide 729 by the smallest prime number possible. You then repeat the same process by taking the result and dividing that number by the smallest prime number. Eventually, you end up with the number 1.

This process creates something called a prime factor tree of 729. The prime numbers used in this tree are the prime factors of 729. Let's look at the prime factor tree for 729:

  • 729 ÷ 3 = 243
  • 243 ÷ 3 = 81
  • 81 ÷ 3 = 27
  • 27 ÷ 3 = 9
  • 9 ÷ 3 = 3
  • 3 ÷ 3 = 1

Put simply, all of the prime numbers that you used to divide above are the prime factors of 729 as well. So what we are left with is the answer to your search, the prime factors of 729:

3, 3, 3, 3, 3, and 3

How Many Prime Factors of 729 Are There?

If we count up all of the prime factors of 729 used in the prime factor tree above, we can see that 729 has a total of 6 prime factors.

Product of Prime Factors of 729

The prime factors shown above (3, 3, 3, 3, 3, and 3) are completely unique to 729. When we multiply all of them together the result will be 729 and this is what we call the product of prime factors of 729. The prime factor products of 729 are listed below:

3 x 3 x 3 x 3 x 3 x 3 = 729

So there you have it. A complete guide to the factors of 729. You should now have the knowledge and skills to go out and calculate your own factors and factor pairs for any number you like.

Feel free to try the calculator below to check another number or, if you're feeling fancy, grab a pencil and paper and try and do it by hand. Just make sure to pick small numbers!

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