Let A be the set of positive dividers of 30°  B be the set of positive dividers of 60° and C the set of positive dividers of 90° then find (A∩B∩C∩)

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.

Let A be the set of positive dividers of 30, B be the set of positive dividers of 60, and C the set of positive dividers of 90. Then find (A ∩ B ∩ C).

Explore how to find the intersection of divisors of 30, 60, and 90 with a step-by-step solution. This problem uses concepts from set theory and number theory, showing the common divisors of the three numbers. Suitable for students in Grades 8-10.

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