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Q: Is 33772 a prime or composite number and how can you show your work?

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It's even. The only even prime number is 2.

Showing a composite number as a product of prime numbers is called prime factorization.

67 is a prime number.

Yes

43 is a prime number whose only factors are itself and one

A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.

It is a composite number because it has at least one positive factor other than one or itself.

6 can be divided by 1, 2, 3 . hence, it is not a prime number, so a composite number.

23 is a prime number so there is no prime factorization. Some consider it to be acceptable to write 1 X 23 in order to show the number is prime, even though 1 is not a prime or composite number.23 is already prime.

Impossible. There is an infinite number of composite numbers.

96 is a composite number because it has more than two factors. 96 is divisible by 2, 4, 1, 96 etc. which clearly shows that it has more than two factors.In order to show that a number is composite there is no need to find its all factors, we have to show only that it has more than two factors.

The proof that there is no largest prime:Assume that there are a finite number of primes for the sake of contradiction. Then, there should be a number P that equals p1p2p3...pn+1. P is either prime or not prime (composite). If it is prime, we just show that P is larger than the largest prime in the list. If it's not prime, it must be composite. Composite always has at least one factor that is prime, but since P is not divisible by any prime in the list, the unknown prime factor(s) must be something not in the list, this also shows that there is a prime larger than the largest prime in the list. Both cases show that no matter how large a list of prime numbers, there will be always at least one larger prime outside of that list.

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