The factors of 378 and the prime factors of 378 differ because three hundred and seventy-eight is a composite number. Also, despite being closely related, the prime factors of 378 and the prime factorization of 378 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 378? and everything else you want to know about the topic.
What are the Factors of 378?
They are: 378, 189, 126, 63, 54, 42, 27, 21, 18, 14, 9, 7, 6, 3, 2, 1. These are all the factors of 378, and every entry in the list can divide 378 without rest (modulo 0). That’s why the terms factors and divisors of 378 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 378, as well as 1 are factors and divisors of 378.
Prime Factors of 378
The prime factors of 378 are the prime numbers which divide 378 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 378 divides the number 378 without any rest, modulo 0.
For 378, the prime factors are: 2, 3, 7. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 378 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 378
The prime factorization of 378 is 2 x 3 x 3 x 3 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 378 does not include the number 1, yet it does include every instance of a certain prime factor.
378 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 378 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 378, 189, 126, 63, 54, 42, 27, 21, 18, 14, 9, 7, 6, 3, 2, 1 and multiply these integers to obtain 378. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 378.
The prime factorization or integer factorization of 378 means determining the set of prime numbers which, when multiplied together, produce the original number 378. This is also known as prime decomposition of 378.
Besides factors for 378, other searched terms on our website include:
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To sum up:
The factors, the prime factors and the prime factorization of 378 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of three hundred and seventy-eight are: 378, 189, 126, 63, 54, 42, 27, 21, 18, 14, 9, 7, 6, 3, 2, 1. The prime factors of three hundred and seventy-eight are 2, 3, 7. And the prime factorization of three hundred and seventy-eight is 2 x 3 x 3 x 3 x 7. Remember that 1 is not a prime factor of 378.
No matter if you had been searching for prime factorization for 378 or prime numbers of 378, you have come to the right page. Also, if you typed what is the prime factorization of 378 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 378 as a product of prime factors or list the factors of 378 will no longer pose a challenge to you.
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