The factors of 840 and the prime factors of 840 differ because eight hundred and forty is a composite number. Also, despite being closely related, the prime factors of 840 and the prime factorization of 840 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 840?* and everything else you want to know about the topic.

## What are the Factors of 840?

They are: 840, 420, 280, 210, 168, 140, 120, 105, 84, 70, 60, 56, 42, 40, 35, 30, 28, 24, 21, 20, 15, 14, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1. These are all the factors of 840, and every entry in the list can divide 840 without rest (modulo 0). That’s why the terms factors and divisors of 840 can be used interchangeably.

As is the case for any natural number greater than zero, the number itself, here 840, as well as 1 are factors and divisors of 840.

## Prime Factors of 840

The prime factors of 840 are the *prime* numbers which divide 840 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 840 divides the number 840 without any rest, modulo 0.

For 840, **the prime factors are: 2, 3, 5, 7**. By definition, 1 is not a prime number.

Besides 1, what sets the factors and the prime factors of the number 840 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.

## Prime Factorization of 840

The prime factorization of 840 is 2 x 2 x 2 x 3 x 5 x 7. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 840 does not include the number 1, yet it does include every instance of a certain prime factor.

840 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 840 have at least two factorizations.

To illustrate what that means select the rightmost and leftmost integer in 840, 420, 280, 210, 168, 140, 120, 105, 84, 70, 60, 56, 42, 40, 35, 30, 28, 24, 21, 20, 15, 14, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1 and multiply these integers to obtain 840. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 840.

The prime factorization or integer factorization of 840 means determining the set of prime numbers which, when multiplied together, produce the original number 840. This is also known as prime decomposition of 840.

Besides factors for 840, 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 840 by using the search form in the sidebar.

To sum up:

The factors, the prime factors and the prime factorization of 840 mean different things, and in strict terms cannot be used interchangeably despite being closely related.

The factors of eight hundred and forty are: 840, 420, 280, 210, 168, 140, 120, 105, 84, 70, 60, 56, 42, 40, 35, 30, 28, 24, 21, 20, 15, 14, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1. The prime factors of eight hundred and forty are 2, 3, 5, 7. And the prime factorization of eight hundred and forty is 2 x 2 x 2 x 3 x 5 x 7. Remember that 1 is not a prime factor of 840.

No matter if you had been searching for prime factorization for 840 or prime numbers of 840, you have come to the right page. Also, if you typed *what is the prime factorization of 840* in the search engine then you are right here, of course.

Taking all of the above into account, tasks including *write 840 as a product of prime factors* or *list the factors of 840* will no longer pose a challenge to you.

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