Question

A positive number is called $n$-primable if it is divisible by $n$ and each of its digits is a one-digit prime number. How many 3-primable positive integers are there that are less than 1000

Answer 1

Single digit primes are 2, 3, 5 and 7. Only 3 is 3-primable
Two digit numbers that are 3-primable are
27, 33, 57, 72, 75
The 3 digit numbers that are 3-primable are
222, 333, 555, 777
225, 252, 522
237, 273, 327, 372, 723, 732
255, 525, 552
357, 375, 537, 573, 735, 753

There are 28 3-primable natural numbers less than 1000