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

 Jun 25, 2021
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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

 Jun 25, 2021

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