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The factors of 189 and the prime factors of 189 differ because hundred and eighty-nine is a composite number. Also, despite being closely related, the prime factors of 189 and the prime factorization of 189 are not exactly the same either.
±1,±3,±7,±9,±21,±27,±63,±189
What are the Factors of 189?
They are: 189, 63, 27, 21, 9, 7, 3, 1. These are all the factors of 189, and every entry in the list can divide 189 without rest (modulo 0). That’s why the terms factors and divisors of 189 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 189, as well as 1 are factors and divisors of 189.
Prime Factors of 189
The prime factors of 189 are the prime numbers which divide 189 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 189 divides the number 189 without any rest, modulo 0.
For 189, 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 189 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 189
The prime factorization of 189 is 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 189 does not include the number 1, yet it does include every instance of a certain prime factor.
189 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 189 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 189, 63, 27, 21, 9, 7, 3, 1 and multiply these integers to obtain 189. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 189.
The prime factorization or integer factorization of 189 means determining the set of prime numbers which, when multiplied together, produce the original number 189. This is also known as prime decomposition of 189.
Besides factors for 189, 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 189 by using the search form in the sidebar.
Summary
To sum up:
The factors of hundred and eighty-nine are: 189, 63, 27, 21, 9, 7, 3, 1. The prime factors of hundred and eighty-nine are 3, 7. And the prime factorization of hundred and eighty-nine is 3 x 3 x 3 x 7. Remember that 1 is not a prime factor of 189.
No matter if you had been searching for prime factorization for 189 or prime numbers of 189, you have come to the right page. Also, if you typed what is the prime factorization of 189 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 189 as a product of prime factors or list the factors of 189 will no longer pose a challenge to you.
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– Article written by Mark, last updated on August 8th, 2023