3. Determine a simple three-digit number whose product of digits is equal to 252.
Solution. By factoring the number 252 into prime factors, we get $252=2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$. By combining the factors of the number 252, we find that the digits of the desired number are $4,9,7$ or $6,6,7$. The desired number is a prime number, so it must be odd, i.e., it could be one of the numbers: $497,947,749,479$, and 667. Upon checking, we find that the numbers 497 and 749 are divisible by 7, and the number 667 is divisible by 23. The prime numbers that satisfy the condition of the problem are 947 and 479.