Answer:
175
Step-by-step explanation:
How would one find a three-digit number which is 5 times as large as the product of its digits?
100a + 10b +c = 5abc
This shows that c must be a multiple of 5. Since it is a digit, c=5 ( c=0 does not work ).
Then:
100a + 10b + 5 = 25ab
This again shows that 10b+5 is a multiple of 25.
By testing all the digits, b=2 or b=7.
If b=2, then
100a + 25 = 50a
which has the solution a= -1/2, not a digit.
if b=7
100a +75 = 175a
Now the solution is a=1, so finally the number is 175. Indeed, 175 = 5*1*7*5.
Does that answer your question..?
