The factors of 364 and the prime factors of 364 differ because three hundred and sixty-four is a composite number. Also, despite being closely related, the prime factors of 364 and the prime factorization of 364 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 364? and everything else you want to know about the topic.
What are the Factors of 364?
They are: 364, 182, 91, 52, 28, 26, 14, 13, 7, 4, 2, 1. These are all the factors of 364, and every entry in the list can divide 364 without rest (modulo 0). That’s why the terms factors and divisors of 364 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 364, as well as 1 are factors and divisors of 364.
Prime Factors of 364
The prime factors of 364 are the prime numbers which divide 364 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 364 divides the number 364 without any rest, modulo 0.
For 364, the prime factors are: 2, 7, 13. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 364 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 364
The prime factorization of 364 is 2 x 2 x 7 x 13. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 364 does not include the number 1, yet it does include every instance of a certain prime factor.
364 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 364 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 364, 182, 91, 52, 28, 26, 14, 13, 7, 4, 2, 1 and multiply these integers to obtain 364. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 364.
The prime factorization or integer factorization of 364 means determining the set of prime numbers which, when multiplied together, produce the original number 364. This is also known as prime decomposition of 364.
Besides factors for 364, 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 364 by using the search form in the sidebar.
To sum up:
The factors, the prime factors and the prime factorization of 364 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of three hundred and sixty-four are: 364, 182, 91, 52, 28, 26, 14, 13, 7, 4, 2, 1. The prime factors of three hundred and sixty-four are 2, 7, 13. And the prime factorization of three hundred and sixty-four is 2 x 2 x 7 x 13. Remember that 1 is not a prime factor of 364.
No matter if you had been searching for prime factorization for 364 or prime numbers of 364, you have come to the right page. Also, if you typed what is the prime factorization of 364 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 364 as a product of prime factors or list the factors of 364 will no longer pose a challenge to you.
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