Prime Factors of 168

Looking to get a list of the prime factors of 168? In this article we'll give you all of the information you need, including the definition of the prime factors of 168, how to calculate the prime factors of 168 (also known as the prime factorization of 168). As a bonus, we'll also list out the prime factor tree of 168 the product of prime factors of 168, and tell you how many prime factors 168 has.

Prime Factors of 168 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 168, 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 168 are all of the prime numbers in it that when multipled together will equal 168.

Let's look at how to find all of the prime factors of 168 and list them out.

How to Find the Prime Factors of 168

You'll often see the process of finding prime factors of 168 referred to as prime factorization. To get the prime factors of 168 we need to divide 168 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 168. The prime numbers used in this tree are the prime factors of 168. Let's look at the prime factor tree for 168:

  • 168 ÷ 2 = 84
  • 84 ÷ 2 = 42
  • 42 ÷ 2 = 21
  • 21 ÷ 3 = 7
  • 7 ÷ 7 = 1

Put simply, all of the prime numbers that you used to divide above are the prime factors of 168 as well. So what we are left with is the answer to your search, the prime factors of 168:

2, 2, 2, 3, and 7

How Many Prime Factors of 168 Are There?

If we count up all of the prime factors of 168 used in the prime factor tree above, we can see that 168 has a total of 5 prime factors.

Product of Prime Factors of 168

The prime factors shown above (2, 2, 2, 3, and 7) are completely unique to 168. When we multiply all of them together the result will be 168 and this is what we call the product of prime factors of 168. The prime factor products of 168 are listed below:

2 x 2 x 2 x 3 x 7 = 168

So there you have it. A complete guide to the factors of 168. 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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Prime Factors of 169