The product of all digits of positive integer M is 105. How many such Ms are there, with four digits?

Step 1: how do we get 105 by multiplying four numbers? Factor it out to primes... 5 x 21 = 5 x 7 x 3 (x 1)

So now we have four numbers 1,3,5,7. How many ways can you arrange 4 numbers? 4 factorial, or 1 x 2 x 3 x 4 = 24