The factors of 684 and the prime factors of 684 differ because six hundred and eighty-four is a composite number. Also, despite being closely related, the prime factors of 684 and the prime factorization of 684 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 684? and everything else you want to know about the topic.
What are the Factors of 684?
They are: 684, 342, 228, 171, 114, 76, 57, 38, 36, 19, 18, 12, 9, 6, 4, 3, 2, 1. These are all the factors of 684, and every entry in the list can divide 684 without rest (modulo 0). That’s why the terms factors and divisors of 684 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 684, as well as 1 are factors and divisors of 684.
Prime Factors of 684
The prime factors of 684 are the prime numbers which divide 684 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 684 divides the number 684 without any rest, modulo 0.
For 684, the prime factors are: 2, 3, 19. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 684 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 684
The prime factorization of 684 is 2 x 2 x 3 x 3 x 19. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 684 does not include the number 1, yet it does include every instance of a certain prime factor.
684 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 684 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 684, 342, 228, 171, 114, 76, 57, 38, 36, 19, 18, 12, 9, 6, 4, 3, 2, 1 and multiply these integers to obtain 684. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 684.
The prime factorization or integer factorization of 684 means determining the set of prime numbers which, when multiplied together, produce the original number 684. This is also known as prime decomposition of 684.
Besides factors for 684, frequently searched terms on our website include:
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To sum up:
The factors, the prime factors and the prime factorization of 684 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of six hundred and eighty-four are: 684, 342, 228, 171, 114, 76, 57, 38, 36, 19, 18, 12, 9, 6, 4, 3, 2, 1. The prime factors of six hundred and eighty-four are 2, 3, 19. And the prime factorization of six hundred and eighty-four is 2 x 2 x 3 x 3 x 19. Remember that 1 is not a prime factor of 684.
No matter if you had been searching for prime factorization for 684 or prime numbers of 684, you have come to the right page. Also, if you typed what is the prime factorization of 684 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 684 as a product of prime factors or list the factors of 684 will no longer pose a challenge to you.
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