Prime Factors of 343

Looking to get a list of the prime factors of 343? In this article we'll give you all of the information you need, including the definition of the prime factors of 343, how to calculate the prime factors of 343 (also known as the prime factorization of 343). As a bonus, we'll also list out the prime factor tree of 343 the product of prime factors of 343, and tell you how many prime factors 343 has.

Prime Factors of 343 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 343, 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 343 are all of the prime numbers in it that when multipled together will equal 343.

Let's look at how to find all of the prime factors of 343 and list them out.

How to Find the Prime Factors of 343

You'll often see the process of finding prime factors of 343 referred to as prime factorization. To get the prime factors of 343 we need to divide 343 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 343. The prime numbers used in this tree are the prime factors of 343. Let's look at the prime factor tree for 343:

  • 343 ÷ 7 = 49
  • 49 ÷ 7 = 7
  • 7 ÷ 7 = 1

Put simply, all of the prime numbers that you used to divide above are the prime factors of 343 as well. So what we are left with is the answer to your search, the prime factors of 343:

7, 7, and 7

How Many Prime Factors of 343 Are There?

If we count up all of the prime factors of 343 used in the prime factor tree above, we can see that 343 has a total of 3 prime factors.

Product of Prime Factors of 343

The prime factors shown above (7, 7, and 7) are completely unique to 343. When we multiply all of them together the result will be 343 and this is what we call the product of prime factors of 343. The prime factor products of 343 are listed below:

7 x 7 x 7 = 343

So there you have it. A complete guide to the factors of 343. 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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