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The prime factorization of 180 is 2x2x3x3x5. Six consecutive prime numbers do not exist in its factorization.
No. The attribute "prime" and "composite" applies only to integers.
Prime numbers are only divisible by 1 and themselves. Since 3 is not a prime number, any prime number divisible by 3 does not exist. Therefore, the set of prime numbers divisible by 3 is an empty set.
There's no reason for them, they just exist. It's like asking, what's the reason for the number 7 ? Prime numbers just happen to be numbers you can't divide by other numbers without getting fractions all over the place. Like 7.
Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.