SOLUTION: A positive integer has three digits. The product of the digits is 135. What is the sum of the digits

Question 959293: A positive integer has three digits. The product of the digits is 135. What is the sum of the digits
Answer by Edwin McCravy(20063) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
The sum of the digits of a nine digit integer is 8.What is the product of these digits... (answered by ankor@dixie-net.com)

Three times the sum of the digits of a positive, two-digit integer is 50 greater than the (answered by lwsshak3,MathTherapy)

The sum of the digits of a positive two-digit integer is 45 less than the integer. What... (answered by ankor@dixie-net.com)

The sum of the digits of a positive two-digit integer is 45 less than the integer. What... (answered by dabanfield)

the hundreds digits of a three digits number is twice its ten digit. its tens digits is... (answered by harpazo)

The sum of the digits of a two-digit number is 12. The product of the digits is three... (answered by rcmcc)

Consider any positive three-digit integer that has all of its digits distinct and none... (answered by ankor@dixie-net.com)

A phone number contains 7 digits. The product of these digits is an even perfect square.... (answered by Alan3354)

The sum of the two digits of a positive integer is 12. When the digits were reversed, the (answered by josgarithmetic,greenestamps,ikleyn)