The factors of 735 and the prime factors of 735 differ because seven hundred and thirty-five is a composite number. Also, despite being closely related, the prime factors of 735 and the prime factorization of 735 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 735? and everything else you want to know about the topic.
What are the Factors of 735?
They are: 735, 245, 147, 105, 49, 35, 21, 15, 7, 5, 3, 1. These are all the factors of 735, and every entry in the list can divide 735 without rest (modulo 0). That’s why the terms factors and divisors of 735 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 735, as well as 1 are factors and divisors of 735.
Prime Factors of 735
The prime factors of 735 are the prime numbers which divide 735 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 735 divides the number 735 without any rest, modulo 0.
For 735, the prime factors are: 3, 5, 7. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 735 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 735
The prime factorization of 735 is 3 x 5 x 7 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 735 does not include the number 1, yet it does include every instance of a certain prime factor.
735 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 735 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 735, 245, 147, 105, 49, 35, 21, 15, 7, 5, 3, 1 and multiply these integers to obtain 735. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 735.
The prime factorization or integer factorization of 735 means determining the set of prime numbers which, when multiplied together, produce the original number 735. This is also known as prime decomposition of 735.
Besides factors for 735, 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 735 by using the search form in the sidebar.
To sum up:
The factors, the prime factors and the prime factorization of 735 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of seven hundred and thirty-five are: 735, 245, 147, 105, 49, 35, 21, 15, 7, 5, 3, 1. The prime factors of seven hundred and thirty-five are 3, 5, 7. And the prime factorization of seven hundred and thirty-five is 3 x 5 x 7 x 7. Remember that 1 is not a prime factor of 735.
No matter if you had been searching for prime factorization for 735 or prime numbers of 735, you have come to the right page. Also, if you typed what is the prime factorization of 735 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 735 as a product of prime factors or list the factors of 735 will no longer pose a challenge to you.
If you have any questions about the factors of seven hundred and thirty-five then fill in the form below and we will respond as soon as possible. If our content concerning all factors of 735 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.