Prime Factors of 1728

Looking to get a list of the prime factors of 1728? In this article we'll give you all of the information you need, including the definition of the prime factors of 1728, how to calculate the prime factors of 1728 (also known as the prime factorization of 1728). As a bonus, we'll also list out the prime factor tree of 1728 the product of prime factors of 1728, and tell you how many prime factors 1728 has.

Prime Factors of 1728 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 1728, 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 1728 are all of the prime numbers in it that when multipled together will equal 1728.

Let's look at how to find all of the prime factors of 1728 and list them out.

How to Find the Prime Factors of 1728

You'll often see the process of finding prime factors of 1728 referred to as prime factorization. To get the prime factors of 1728 we need to divide 1728 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 1728. The prime numbers used in this tree are the prime factors of 1728. Let's look at the prime factor tree for 1728:

  • 1728 ÷ 2 = 864
  • 864 ÷ 2 = 432
  • 432 ÷ 2 = 216
  • 216 ÷ 2 = 108
  • 108 ÷ 2 = 54
  • 54 ÷ 2 = 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 1728 as well. So what we are left with is the answer to your search, the prime factors of 1728:

2, 2, 2, 2, 2, 2, 3, 3, and 3

How Many Prime Factors of 1728 Are There?

If we count up all of the prime factors of 1728 used in the prime factor tree above, we can see that 1728 has a total of 9 prime factors.

Product of Prime Factors of 1728

The prime factors shown above (2, 2, 2, 2, 2, 2, 3, 3, and 3) are completely unique to 1728. When we multiply all of them together the result will be 1728 and this is what we call the product of prime factors of 1728. The prime factor products of 1728 are listed below:

2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 1728

So there you have it. A complete guide to the factors of 1728. 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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