Prime Factors of 825

Looking to get a list of the prime factors of 825? In this article we'll give you all of the information you need, including the definition of the prime factors of 825, how to calculate the prime factors of 825 (also known as the prime factorization of 825). As a bonus, we'll also list out the prime factor tree of 825 the product of prime factors of 825, and tell you how many prime factors 825 has.

Prime Factors of 825 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 825, 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 825 are all of the prime numbers in it that when multipled together will equal 825.

Let's look at how to find all of the prime factors of 825 and list them out.

How to Find the Prime Factors of 825

You'll often see the process of finding prime factors of 825 referred to as prime factorization. To get the prime factors of 825 we need to divide 825 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 825. The prime numbers used in this tree are the prime factors of 825. Let's look at the prime factor tree for 825:

  • 825 ÷ 3 = 275
  • 275 ÷ 5 = 55
  • 55 ÷ 5 = 11
  • 11 ÷ 11 = 1

Put simply, all of the prime numbers that you used to divide above are the prime factors of 825 as well. So what we are left with is the answer to your search, the prime factors of 825:

3, 5, 5, and 11

How Many Prime Factors of 825 Are There?

If we count up all of the prime factors of 825 used in the prime factor tree above, we can see that 825 has a total of 4 prime factors.

Product of Prime Factors of 825

The prime factors shown above (3, 5, 5, and 11) are completely unique to 825. When we multiply all of them together the result will be 825 and this is what we call the product of prime factors of 825. The prime factor products of 825 are listed below:

3 x 5 x 5 x 11 = 825

So there you have it. A complete guide to the factors of 825. 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!

Cite, Link, or Reference This Page

If you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it. We really appreciate your support!

  • "Prime Factors of 825". Accessed on October 2, 2023.

  • "Prime Factors of 825"., Accessed 2 October, 2023.

  • Prime Factors of 825. Retrieved from

Prime Factors Calculator

Want to find the prime factor for another number? Enter your number below and click calculate.

Find Prime Factors

Next Prime Factor Calculation

Eager to continue your learning of prime factorization? Why not try the next number on our list and see if you can calculate the prime factors of it for yourself?

Prime Factors of 826