Question

Let X be a four - digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?

Accepted Answer

A. For the product of 4 single digits to be prime, three of the digits must be 1 and one digit must be a prime number (2, 3, 5, or 7). Since the unit digit of X must be prime, the unit digit can be 2, 3, 5, or 7. The remaining three digits (thousands, hundreds, tens) must all be 1. Thus, the only possible numbers are 1112, 1113, 1115, and 1117. Total = 4.

Prime Product 4-digit Integers

Explanation

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