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The factors of 165 and the prime factors of 165 differ because hundred and sixty-five is a composite number. Also, despite being closely related, the prime factors of 165 and the prime factorization of 165 are not exactly the same either.
±1,±3,±5,±11,±15,±33,±55,±165
What are the Factors of 165?
They are: 165, 55, 33, 15, 11, 5, 3, 1. These are all the factors of 165, and every entry in the list can divide 165 without rest (modulo 0). That’s why the terms factors and divisors of 165 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 165, as well as 1 are factors and divisors of 165.
Prime Factors of 165
The prime factors of 165 are the prime numbers which divide 165 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 165 divides the number 165 without any rest, modulo 0.
For 165, the prime factors are: 3, 5, 11. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 165 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 165
The prime factorization of 165 is 3 x 5 x 11. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 165 does not include the number 1, yet it does include every instance of a certain prime factor.
165 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 165 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 165, 55, 33, 15, 11, 5, 3, 1 and multiply these integers to obtain 165. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 165.
The prime factorization or integer factorization of 165 means determining the set of prime numbers which, when multiplied together, produce the original number 165. This is also known as prime decomposition of 165.
Besides factors for 165, 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 165 by using the search form in the sidebar.
Summary
To sum up:
The factors of hundred and sixty-five are: 165, 55, 33, 15, 11, 5, 3, 1. The prime factors of hundred and sixty-five are 3, 5, 11. And the prime factorization of hundred and sixty-five is 3 x 5 x 11. Remember that 1 is not a prime factor of 165.
No matter if you had been searching for prime factorization for 165 or prime numbers of 165, you have come to the right page. Also, if you typed what is the prime factorization of 165 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 165 as a product of prime factors or list the factors of 165 will no longer pose a challenge to you.
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– Article written by Mark, last updated on August 8th, 2023