How many prime positive integers are divisors of 555?
One way to do this is to start with the smallest prime number, 2, and see if it divides 555 evenly. If I divide 555 by 2, I get a decimal, not an integer, so 2 is not a factor of 555. The next smallest prime number is 3, so I can try to divide 555 by 3. If I divide 555 by 3, I get 185, which is an integer, so 3 is a factor of 555. Now I can write 555 as 3 times 185, and try to factor 185 further. Again, I can start with the smallest prime number, 2, and see if it divides 185 evenly. If I divide 185 by 2, I get a decimal, not an integer, so 2 is not a factor of 185. The next smallest prime number is 3, so I can try to divide 185 by 3. If I divide 185 by 3, I get a decimal, not an integer, so 3 is not a factor of 185. The next smallest prime number is 5, so I can try to divide 185 by 5. If I divide 185 by 5, I get 37, which is an integer, so 5 is a factor of 185. Now I can write 185 as 5 times 37, and try to factor 37 further. However, 37 is already a prime number, so it cannot be factored further. Therefore, I have found all the prime factors of 555, which are 3, 5, and 37. The number of prime factors is 3. 