The factors of 31 and the prime factors of 31 don’t differ much because thirty-one is a prime number. But, despite being closely related, the prime factors of 31 and the prime factorization of 31 are not exactly the same. By reading on you can learn the answer to the question *what are the factors of 31?* and everything else you want to know about the topic.

## What are the Factors of 31?

They are: 31, 1. These are all the factors of 31, and every entry in the list can divide 31 without rest (modulo 0). That’s why the terms factors and divisors of 31 can be used interchangeably.

As is the case for any natural number greater than zero, the number itself, here 31, as well as 1 are factors and divisors of 31.

## Prime Factors of 31

The prime factors of 31 are the *prime* numbers which divide 31 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 31 divides the number 31 without any rest, modulo 0.

For 31, **the prime factor is: 31**. By definition, 1 is not a prime number.

Besides 1, what sets the factors and the prime factors of the number 31 apart is the word “prime”. For non-prime numbers the former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.

## Prime Factorization of 31

The prime factorization of 31 is 31. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 31 does not include the number 1, yet it does include every instance of a certain prime factor.

31 is a prime number. In contrast to composite numbers which have at the least two factorizations, prime numbers like 31 only have one factorization.

The prime factorization or integer factorization of 31 means determining the set of prime numbers which, when multiplied together, produce the original number 31. This is also known as prime decomposition of 31.

Besides factors for 31, 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 31 by using the search form in the sidebar.

To sum up:

The factors, the prime factors and the prime factorization of 31 mean different things, and in strict terms cannot be used interchangeably despite being closely related.

The factors of thirty-one are: 31, 1. The prime factor of thirty-one is 31. And the prime factorization of thirty-one is 31. Remember that 1 is not a prime factor of 31.

No matter if you had been searching for prime factorization for 31 or prime numbers of 31, you have come to the right page. Also, if you typed *what is the prime factorization of 31* in the search engine then you are right here, of course.

Taking all of the above into account, tasks including *write 31 as a product of prime factors* or *list the factors of 31* will no longer pose a challenge to you.

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