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

 Feb 16, 2022
 #1
avatar+2438 
0

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

 Feb 16, 2022
 #2
avatar+117834 
0

Good logic BuilderBoi,

But I think those 4 digits can be in any order ....

Melody  Feb 16, 2022
 #3
avatar+36433 
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
avatar+2438 
+1

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

 

Thanks Melody and Pavlov!!!

BuilderBoi  Feb 16, 2022

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