The factors of 289 and the prime factors of 289 differ because two hundred and eighty-nine is a composite number. Also, despite being closely related, the prime factors of 289 and the prime factorization of 289 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 289? and everything else you want to know about the topic.
What are the Factors of 289?
They are: 289, 17, 1. These are all the factors of 289, and every entry in the list can divide 289 without rest (modulo 0). That’s why the terms factors and divisors of 289 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 289, as well as 1 are factors and divisors of 289.
Prime Factors of 289
The prime factors of 289 are the prime numbers which divide 289 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 289 divides the number 289 without any rest, modulo 0.
For 289, the prime factors are: 17. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 289 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 289
The prime factorization of 289 is 17 x 17. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 289 does not include the number 1, yet it does include every instance of a certain prime factor.
289 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 289 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 289, 17, 1 and multiply these integers to obtain 289. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 289.
The prime factorization or integer factorization of 289 means determining the set of prime numbers which, when multiplied together, produce the original number 289. This is also known as prime decomposition of 289.
Besides factors for 289, 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 289 by using the search form in the sidebar.
To sum up:
The factors, the prime factors and the prime factorization of 289 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of two hundred and eighty-nine are: 289, 17, 1. The prime factors of two hundred and eighty-nine are 17. And the prime factorization of two hundred and eighty-nine is 17 x 17. Remember that 1 is not a prime factor of 289.
No matter if you had been searching for prime factorization for 289 or prime numbers of 289, you have come to the right page. Also, if you typed what is the prime factorization of 289 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 289 as a product of prime factors or list the factors of 289 will no longer pose a challenge to you.
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