SOLUTION: What five different whole numbers add up to 18 multiply those same numbers and get 240?

Question 731432: What five different whole numbers add up to 18 multiply those same numbers and get 240?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE ANSWER:

HOW TO GET TO THE ANSWER:
We need to find factors of 240.
Either systematically or sloppily.
Systematically:
prime factorization that can be obtained by dividing over and over by prime numbers in order, starting from 2 and going up:
240 � = 120
120 � = 60
60 � = 30
30 � = 15
15 � =
So 240 = XXXXX
The sloppy way:
I know that 240 = 30 X 8, so

Then, it's a question of turning the 6 factors in into five factors by grouping (multiplying) some together, and maybe including a 1 as a factor.
If we do not include a 1, to add up to the even number 18, we could have both odd factors (3 and 5) by themselves, adding to 12, or both paired with a 2, to become even numbers.
Neither choice works.
With 3 and 5 as two of the five different whole numbers, we have
and the four remaining 2's cannot be grouped into the three additional different whole numbers.
Using and as two of the five different whole numbers is not possible either, because we would just have two extra 2's to make three additional whole numbers from.
With as one of the five different whole numbers, what would we do with and ?
We need one and only one additional odd number.
The other odd number must be turned into an even number by grouping it with a 2.
We would be left with three 2's to be turned into the two additional different whole numbers.
Those two additional different whole numbers can only be and
What do we do with and ?
and as two of the five different whole numbers is an obvious choice, because using and would make the sum too large:
.
So , , , , and are the five different whole numbers that multiply to yield 240,
,
and
is the 5-number sum.
RELATED QUESTIONS
What two numbers multiply to get -240 and add to get... (answered by jim_thompson5910)

what two numbers multiply to -240 and add to... (answered by god2012)

Three whole numbers add up to 149 and multiply to give 987. What is the largest of the... (answered by ikleyn)

what numbers add to -18 and multiply to... (answered by JulietG)

what are the five consecutive whole numbers that add up to... (answered by drj)

what 2 numbers add up to -126 but multiply to get... (answered by Alan3354,JBarnum)

what two numbers multiply to get -24 but also add up to... (answered by solver91311)

what two numbers can you add to get-60 and multiply to get... (answered by stanbon)

What numbers add to get -14 and multiply to get 49 (answered by stanbon)