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The factors of 972 and the prime factors of 972 differ because nine hundred and seventy-two is a composite number. Also, despite being closely related, the prime factors of 972 and the prime factorization of 972 are not exactly the same either.
±1,±2,±3,±4,±6,±9,±12,±18,±27,±36,±54,±81,±108,±162,±243,±324,±486,±972
What are the Factors of 972?
They are: 972, 486, 324, 243, 162, 108, 81, 54, 36, 27, 18, 12, 9, 6, 4, 3, 2, 1. These are all the factors of 972, and every entry in the list can divide 972 without rest (modulo 0). That’s why the terms factors and divisors of 972 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 972, as well as 1 are factors and divisors of 972.
Prime Factors of 972
The prime factors of 972 are the prime numbers which divide 972 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 972 divides the number 972 without any rest, modulo 0.
For 972, 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 972 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 972
The prime factorization of 972 is 2 x 2 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 972 does not include the number 1, yet it does include every instance of a certain prime factor.
972 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 972 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 972, 486, 324, 243, 162, 108, 81, 54, 36, 27, 18, 12, 9, 6, 4, 3, 2, 1 and multiply these integers to obtain 972. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 972.
The prime factorization or integer factorization of 972 means determining the set of prime numbers which, when multiplied together, produce the original number 972. This is also known as prime decomposition of 972.
Besides factors for 972, other searched terms on our website include:
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Summary
To sum up:
The factors of nine hundred and seventy-two are: 972, 486, 324, 243, 162, 108, 81, 54, 36, 27, 18, 12, 9, 6, 4, 3, 2, 1. The prime factors of nine hundred and seventy-two are 2, 3. And the prime factorization of nine hundred and seventy-two is 2 x 2 x 3 x 3 x 3 x 3 x 3. Remember that 1 is not a prime factor of 972.
No matter if you had been searching for prime factorization for 972 or prime numbers of 972, you have come to the right page. Also, if you typed what is the prime factorization of 972 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 972 as a product of prime factors or list the factors of 972 will no longer pose a challenge to you.
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– Article written by Mark, last updated on August 8th, 2023