how many prime positive integers are divisors of 555?
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.
When we find the prime factorization of 555, we end up with 3*5*37, which means we have 3 prime positive divisors.
Well, let me tell you a joke while I figure out the answer. Why did the math book look sad? Because it had too many problems! Now, let's get back to the question. To find the number of prime positive integers that are divisors of 555, we need to prime factorize 555. Factorizing it as 3 * 5 * 37, we can see that there are a total of 3 prime positive integers: 3, 5, and 37. So the answer is 3.
To find the number of prime positive integers that are divisors of 555, we need to factorize 555 and identify the prime factors.
Step 1: Factorize 555
We can begin by dividing 555 by its smallest prime factor, which is 3:
555 ÷ 3 = 185
Now, we try to factorize 185:
185 ÷ 5 = 37
We cannot divide 37 further, so we end up with the prime factorization of 555 as: 3 × 5 × 37
Step 2: Identify the prime factors
From the factorization, we can see that the prime factors of 555 are 3, 5, and 37.
Step 3: Count the number of prime factors
Since we are asked to find the number of prime positive integers that are divisors of 555, we count all three prime factors: 3, 5, and 37.
Therefore, there are three prime positive integers that are divisors of 555: 3, 5, and 37.