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

Guest Feb 16, 2022

#1**+1 **

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

BuilderBoi Feb 16, 2022

#3**0 **

....building on this great answer there are 4 * 3 * 2 possibles = 24

5731

5713

5173

5137

7531

7513

etc .....

ElectricPavlov
Feb 16, 2022

#4**+2 **

Gahh... 4 x 3 x 2 = \(\color{brown}\boxed{24}\) possible ways.

Thanks Melody and Pavlov!!!

BuilderBoi
Feb 16, 2022