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