A positive integer has three digits. The product of the digits is 135.
What is the sum of the digits
Break 135 into a product of primes:
135 = 3*3*3*5
That's a product of four digits, not three. To reduce it to three,
we'll have to multiply two of them together and take their product
as a digit. The only way to multiply two of those together to get
a single digit is to multiply two of the 3's together as having a
factor of 9. That is, the digits have to be 3,5, and 9. So the
sum of the digits is 3+5+9 = 17.
Edwin
