CAT 2025 Slot 1 QA Question 9: In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum p

Question

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum p

Accepted Answer

The non-zero perfect-square digits are 1, 4 and 9. Hence, these cannot be used.
The available digits are 2, 3, 5, 6, 7 and 8.
Among these, the prime digits are 2, 3, 5 and 7, while the non-prime digits are 6 and 8.

Since exactly one digit must be prime, the number must contain both 6 and 8, and one

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is