The product of all digits of positive integer M is 105. How many such Ms are there with four digits?
+2668 The prime factorization of 105 is: 5 x 7 x 3
Because there are only 3 prime factors, the 4th digit must be a 1. This makes for \(\color{brown}\boxed4\) possible M's
+118687 Good logic BuilderBoi,
But I think those 4 digits can be in any order ....
+37155 ....building on this great answer there are 4 * 3 * 2 possibles = 24
5731
5713
5173
5137
7531
7513
etc .....
+2668 Gahh... 4 x 3 x 2 = \(\color{brown}\boxed{24}\) possible ways.
Thanks Melody and Pavlov!!!
