The factors of 420 and the prime factors of 420 differ because four hundred and twenty is a composite number. Also, despite being closely related, the prime factors of 420 and the prime factorization of 420 are not exactly the same either. In any case, by reading on you can learn the answer to the question what are the factors of 420? and everything else you want to know about the topic.
What are the Factors of 420?
They are: 420, 210, 140, 105, 84, 70, 60, 42, 35, 30, 28, 21, 20, 15, 14, 12, 10, 7, 6, 5, 4, 3, 2, 1. These are all the factors of 420, and every entry in the list can divide 420 without rest (modulo 0). That’s why the terms factors and divisors of 420 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 420, as well as 1 are factors and divisors of 420.
Prime Factors of 420
The prime factors of 420 are the prime numbers which divide 420 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 420 divides the number 420 without any rest, modulo 0.
For 420, the prime factors are: 2, 3, 5, 7. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 420 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 420
The prime factorization of 420 is 2 x 2 x 3 x 5 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 420 does not include the number 1, yet it does include every instance of a certain prime factor.
420 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 420 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 420, 210, 140, 105, 84, 70, 60, 42, 35, 30, 28, 21, 20, 15, 14, 12, 10, 7, 6, 5, 4, 3, 2, 1 and multiply these integers to obtain 420. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 420.
The prime factorization or integer factorization of 420 means determining the set of prime numbers which, when multiplied together, produce the original number 420. This is also known as prime decomposition of 420.
Besides factors for 420, frequently searched terms on our website include:
We did not place any calculator here as there are already a plethora of them on the web. But you can find the factors, prime factors and the factorizations of many numbers including 420 by using the search form in the sidebar.
To sum up:
The factors, the prime factors and the prime factorization of 420 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of four hundred and twenty are: 420, 210, 140, 105, 84, 70, 60, 42, 35, 30, 28, 21, 20, 15, 14, 12, 10, 7, 6, 5, 4, 3, 2, 1. The prime factors of four hundred and twenty are 2, 3, 5, 7. And the prime factorization of four hundred and twenty is 2 x 2 x 3 x 5 x 7. Remember that 1 is not a prime factor of 420.
No matter if you had been searching for prime factorization for 420 or prime numbers of 420, you have come to the right page. Also, if you typed what is the prime factorization of 420 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 420 as a product of prime factors or list the factors of 420 will no longer pose a challenge to you.
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