The factors of 343 and the prime factors of 343 differ because three hundred and forty-three is a composite number. Also, despite being closely related, the prime factors of 343 and the prime factorization of 343 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 343? and everything else you want to know about the topic.
What are the Factors of 343?
They are: 343, 49, 7, 1. These are all the factors of 343, and every entry in the list can divide 343 without rest (modulo 0). That’s why the terms factors and divisors of 343 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 343, as well as 1 are factors and divisors of 343.
Prime Factors of 343
The prime factors of 343 are the prime numbers which divide 343 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 343 divides the number 343 without any rest, modulo 0.
For 343, the prime factors are: 7. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 343 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 343
The prime factorization of 343 is 7 x 7 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 343 does not include the number 1, yet it does include every instance of a certain prime factor.
343 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 343 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 343, 49, 7, 1 and multiply these integers to obtain 343. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 343.
The prime factorization or integer factorization of 343 means determining the set of prime numbers which, when multiplied together, produce the original number 343. This is also known as prime decomposition of 343.
Besides factors for 343, frequently 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 343 by using the search form in the sidebar.
To sum up:
The factors, the prime factors and the prime factorization of 343 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of three hundred and forty-three are: 343, 49, 7, 1. The prime factors of three hundred and forty-three are 7. And the prime factorization of three hundred and forty-three is 7 x 7 x 7. Remember that 1 is not a prime factor of 343.
No matter if you had been searching for prime factorization for 343 or prime numbers of 343, you have come to the right page. Also, if you typed what is the prime factorization of 343 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 343 as a product of prime factors or list the factors of 343 will no longer pose a challenge to you.
If you have any questions about the factors of three hundred and forty-three then fill in the form below and we will respond as soon as possible. If our content concerning all factors of 343 has been of help to you then share it by means of pressing the social buttons. And don’t forget to bookmark us.
Thanks for your visit.