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