Solution:

Finding the Common Divisor:
To find the greatest number that divides 17, 42, and 93 and leaves remainders of 4, 3, and 2 respectively, we need to first find the common divisor of the differences between the numbers and their corresponding remainders.
We calculate the differences as follows:
- (17 - 4) = 13
- (42 - 3) = 39
- (93 - 2) = 91

Calculating Common Divisor:
Now, we find the greatest common divisor of these differences:
- Factors of 13: 1, 13
- Factors of 39: 1, 3, 13, 39
- Factors of 91: 1, 7, 13, 91
The greatest common divisor of 13, 39, and 91 is 13. Therefore, the greatest number that divides 17, 42, and 93 and leaves remainders of 4, 3, and 2 respectively is 13.

Explanation:
When we divide 17 by 13, we get a quotient of 1 and a remainder of 4. Similarly, when we divide 42 by 13, we get a quotient of 3 and a remainder of 3. Finally, when we divide 93 by 13, we get a quotient of 7 and a remainder of 2. This confirms that 13 is the greatest number that satisfies the given conditions.