To solve this, we first find the positive divisors of each number and then determine their intersection.

Step 1: Find divisors of each number

1. Divisors of 30: $1, 2, 3, 5, 6, 10, 15, 30$
2. Divisors of 60: $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$
3. Divisors of 90: $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 2: Find the intersection of these sets

We take the common divisors in all three sets:

$A \cap B \cap C = \{1, 2, 3, 5, 6, 10, 15, 30\}$

Answer

The intersection $A \cap B \cap C$ is: $\{1, 2, 3, 5, 6, 10, 15, 30\}$

Would you like further details on the steps?

Here are 5 related questions to explore this concept:

1. What are the divisors of 120, and how would they intersect with $A \cap B \cap C$?
2. How can we find the intersection of divisors of more than three numbers systematically?
3. Why are prime factors useful in finding common divisors?
4. What are the divisors of a prime number like 7, and how does it affect intersections?
5. How would this method change if we considered only odd divisors?

Tip: To find common divisors, breaking numbers into prime factors can help quickly identify shared factors across multiple sets.