Find a three digit number so that when the digita of the number Are added together the total is one fifth of the product of the digits

Answer 1

if the digits are a,b,c then

5(a+b+c) = abc
c = 5(a+b)/(ab-5)

so, ab must be greater than 5,

ab cannot be 6, since then a+b > 5
if ab=7, then 5(8)/2 = 20 > 10
if ab=8, then c = 5(6)/3 = 10 too big
if ab=9, then c=5(6)/4 = not integer
if ab=10, then c=5(7)/5 = 7

257: 2+5+7 = 14 = 2*5*7/5