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The factors of 975 and the prime factors of 975 differ because nine hundred and seventy-five is a composite number. Also, despite being closely related, the prime factors of 975 and the prime factorization of 975 are not exactly the same either.
What are the Factors of 975?
They are: 975, 325, 195, 75, 65, 39, 25, 15, 13, 5, 3, 1. These are all the factors of 975, and every entry in the list can divide 975 without rest (modulo 0). That’s why the terms factors and divisors of 975 can be used interchangeably.
As is the case for any natural number greater than zero, the number itself, here 975, as well as 1 are factors and divisors of 975.
Prime Factors of 975
The prime factors of 975 are the prime numbers which divide 975 exactly, without remainder as defined by the Euclidean division. In other words, a prime factor of 975 divides the number 975 without any rest, modulo 0.
For 975, the prime factors are: 3, 5, 13. By definition, 1 is not a prime number.
Besides 1, what sets the factors and the prime factors of the number 975 apart is the word “prime”. The former list contains both, composite and prime numbers, whereas the latter includes only prime numbers.
Prime Factorization of 975
The prime factorization of 975 is 3 x 5 x 5 x 13. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 975 does not include the number 1, yet it does include every instance of a certain prime factor.
975 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 975 have at least two factorizations.
To illustrate what that means select the rightmost and leftmost integer in 975, 325, 195, 75, 65, 39, 25, 15, 13, 5, 3, 1 and multiply these integers to obtain 975. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 975.
The prime factorization or integer factorization of 975 means determining the set of prime numbers which, when multiplied together, produce the original number 975. This is also known as prime decomposition of 975.
Besides factors for 975, other searched terms on our website include:
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To sum up:
The factors of nine hundred and seventy-five are: 975, 325, 195, 75, 65, 39, 25, 15, 13, 5, 3, 1. The prime factors of nine hundred and seventy-five are 3, 5, 13. And the prime factorization of nine hundred and seventy-five is 3 x 5 x 5 x 13. Remember that 1 is not a prime factor of 975.
No matter if you had been searching for prime factorization for 975 or prime numbers of 975, you have come to the right page. Also, if you typed what is the prime factorization of 975 in the search engine then you are right here, of course.
Taking all of the above into account, tasks including write 975 as a product of prime factors or list the factors of 975 will no longer pose a challenge to you.
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