The factors of 729 and the prime factors of 729 differ because seven hundred and twenty-nine is a composite number. Also, despite being closely related, the prime factors of 729 and the prime factorization of 729 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 729? and everything else you want to know about the topic.
What are the Factors of 729?
They are: 729, 243, 81, 27, 9, 3, 1. These are all the factors of 729, and every entry in the list can divide 729 without rest (modulo 0). That’s why the terms factors and divisors of 729 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 729, as well as 1 are factors and divisors of 729.
Prime Factors of 729
The prime factors of 729 are the prime numbers which divide 729 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 729 divides the number 729 without any rest, modulo 0.
For 729, the prime factors are: 3. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 729 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 729
The prime factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 729 does not include the number 1, yet it does include every instance of a certain prime factor.
729 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 729 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 729, 243, 81, 27, 9, 3, 1 and multiply these integers to obtain 729. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 729.
The prime factorization or integer factorization of 729 means determining the set of prime numbers which, when multiplied together, produce the original number 729. This is also known as prime decomposition of 729.
Besides factors for 729, other searched terms on our website include:
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To sum up:
The factors, the prime factors and the prime factorization of 729 mean different things, and in strict terms cannot be used interchangeably despite being closely related.
The factors of seven hundred and twenty-nine are: 729, 243, 81, 27, 9, 3, 1. The prime factors of seven hundred and twenty-nine are 3. And the prime factorization of seven hundred and twenty-nine is 3 x 3 x 3 x 3 x 3 x 3. Remember that 1 is not a prime factor of 729.
No matter if you had been searching for prime factorization for 729 or prime numbers of 729, you have come to the right page. Also, if you typed what is the prime factorization of 729 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 729 as a product of prime factors or list the factors of 729 will no longer pose a challenge to you.
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