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The factors of 12 and the prime factors of 12 differ because twelve is a composite number. Also, despite being closely related, the prime factors of 12 and the prime factorization of 12 are not exactly the same either.
±1,±2,±3,±4,±6,±12
What are the Factors of 12?
They are: 12, 6, 4, 3, 2, 1. These are all the factors of 12, and every entry in the list can divide 12 without rest (modulo 0). That’s why the terms factors and divisors of 12 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 12, as well as 1 are factors and divisors of 12.
Prime Factors of 12
The prime factors of 12 are the prime numbers which divide 12 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 12 divides the number 12 without any rest, modulo 0.
For 12, the prime factors are: 2, 3. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 12 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 12
The prime factorization of 12 is 2 x 2 x 3. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 12 does not include the number 1, yet it does include every instance of a certain prime factor.
12 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 12 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 12, 6, 4, 3, 2, 1 and multiply these integers to obtain 12. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 12.
The prime factorization or integer factorization of 12 means determining the set of prime numbers which, when multiplied together, produce the original number 12. This is also known as prime decomposition of 12.
Besides factors for 12, 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 12 by using the search form in the sidebar.
Summary
To sum up:
The factors of twelve are: 12, 6, 4, 3, 2, 1. The prime factors of twelve are 2, 3. And the prime factorization of twelve is 2 x 2 x 3. Remember that 1 is not a prime factor of 12.
No matter if you had been searching for prime factorization for 12 or prime numbers of 12, you have come to the right page. Also, if you typed what is the prime factorization of 12 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 12 as a product of prime factors or list the factors of 12 will no longer pose a challenge to you.
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– Article written by Mark, last updated on August 8th, 2023