Prime Factors of 420
Looking to get a list of the prime factors of 420? In this article we'll give you all of the information you need, including the definition of the prime factors of 420, how to calculate the prime factors of 420 (also known as the prime factorization of 420). As a bonus, we'll also list out the prime factor tree of 420 the product of prime factors of 420, and tell you how many prime factors 420 has.
Prime Factors of 420 Definition
Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 420, 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 420 are all of the prime numbers in it that when multipled together will equal 420.
Let's look at how to find all of the prime factors of 420 and list them out.
How to Find the Prime Factors of 420
You'll often see the process of finding prime factors of 420 referred to as prime factorization. To get the prime factors of 420 we need to divide 420 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 420. The prime numbers used in this tree are the prime factors of 420. Let's look at the prime factor tree for 420:
- 420 ÷ 2 = 210
- 210 ÷ 2 = 105
- 105 ÷ 3 = 35
- 35 ÷ 5 = 7
- 7 ÷ 7 = 1
Put simply, all of the prime numbers that you used to divide above are the prime factors of 420 as well. So what we are left with is the answer to your search, the prime factors of 420:
2, 2, 3, 5, and 7
How Many Prime Factors of 420 Are There?
If we count up all of the prime factors of 420 used in the prime factor tree above, we can see that 420 has a total of 5 prime factors.
Product of Prime Factors of 420
The prime factors shown above (2, 2, 3, 5, and 7) are completely unique to 420. When we multiply all of them together the result will be 420 and this is what we call the product of prime factors of 420. The prime factor products of 420 are listed below:
2 x 2 x 3 x 5 x 7 = 420
So there you have it. A complete guide to the factors of 420. 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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