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The factors of 36 and the prime factors of 36 differ because thirty-six is a composite number. Also, despite being closely related, the prime factors of 36 and the prime factorization of 36 are not exactly the same either.
±1,±2,±3,±4,±6,±9,±12,±18,±36
What are the Factors of 36?
They are: 36, 18, 12, 9, 6, 4, 3, 2, 1. These are all the factors of 36, and every entry in the list can divide 36 without rest (modulo 0). That’s why the terms factors and divisors of 36 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 36, as well as 1 are factors and divisors of 36.
Prime Factors of 36
The prime factors of 36 are the prime numbers which divide 36 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 36 divides the number 36 without any rest, modulo 0.
For 36, the prime factors are: 2, 3. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 36 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 36
The prime factorization of 36 is 2 x 2 x 3 x 3. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 36 does not include the number 1, yet it does include every instance of a certain prime factor.
36 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 36 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 36, 18, 12, 9, 6, 4, 3, 2, 1 and multiply these integers to obtain 36. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 36.
The prime factorization or integer factorization of 36 means determining the set of prime numbers which, when multiplied together, produce the original number 36. This is also known as prime decomposition of 36.
Besides factors for 36, other 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 36 by using the search form in the sidebar.
Summary
To sum up:
The factors of thirty-six are: 36, 18, 12, 9, 6, 4, 3, 2, 1. The prime factors of thirty-six are 2, 3. And the prime factorization of thirty-six is 2 x 2 x 3 x 3. Remember that 1 is not a prime factor of 36.
No matter if you had been searching for prime factorization for 36 or prime numbers of 36, you have come to the right page. Also, if you typed what is the prime factorization of 36 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 36 as a product of prime factors or list the factors of 36 will no longer pose a challenge to you.
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– Article written by Mark, last updated on August 8th, 2023