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Find the smallest two-digit number where the product of its two digits is equal to half the number.

 Dec 7, 2020
 #1
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36 is the smallest such number:

 

3  x  6 =18

36 / 2 =18

 Dec 7, 2020
 #2
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(a (10)   +  b )   / 2   =   ab

 

10a  + b  = 2ab

 

10a =    2ab - b

 

10a  =   b ( 2a - 1)

 

b =   10a  / ( 2a  -1)

 

b will be the smallest possible   integer, 6,  when a = 3

 

So....the  number  = 36.....just as the Guest  found  !!!

 

cool cool cool

 Dec 8, 2020

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