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

 Oct 28, 2021
 #1
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There are 24 such numbers as follows:

 

1357 , 1375 , 1537 , 1573 , 1735 , 1753 , 3157 , 3175 , 3517 , 3571 , 3715 , 3751 , 5137 , 5173 , 5317 , 5371 , 5713 , 5731 , 7135 , 7153 , 7315 , 7351 , 7513 , 7531 , Total =  24 such numbers

 Oct 28, 2021
 #2
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Prime factorization

 

105 = 5  x   3   x 7         the fourth digit can only be a ' 1 '

 

the four digits are   5 3 7 1    which can be aranged in    4 x 3 x 2 x 1 ways = 24 numbers

 Oct 28, 2021

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