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?

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

4. Given that unit digit of X X X and product of all 4 digits of X X X are prime. The product of two numbers to be prime is possible only when one of the numbers is prime and the other is ‘1’. The possibilities for the prime unit digits are - 2,3,5,7 (Note that 1 is not a prime number) Hence the possib