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