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

 May 9, 2021
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Prime factor of 105 -> 3*5*7

The number has 3, 5, 7, and 1

These are 4 distinct, so there are 4! ways

this is the only case b/c there is no multiplication of 3,5,7 that is 1 digit

The answer is 4!

laugh


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