Start with the product solutions, and if nothing seems pliable, start backwards and work with the sum results.

For the hard one, 612 is not an easy number to find, but basic math shows that 6+1+2=9 so the number is divisible by 3 (and I won't go any farther to prevent spoiling it) Finding a system by which you create the situations that allow the operands and factors to be discovered while also flexing your basic math skills is the fun of the game.