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how many prime positive integers are divisors of 555?

  • math -

    An obvious candidate is 5, so if you divide 555 by 5 you'll get 111. That's divisible by 3 (because the sum of the digits is divisible by 3, which is a useful quick check), so do that and you'll get 111/3 = 37. But 37 is a prime number, so you won't be able to find any more. So there should be just three, i.e. 3, 5 and 37.

  • math -

    When we find the prime factorization of 555, we end up with 3*5*37, which means we have 3 prime positive divisors.

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