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