Is this even a real math question?

[Kaitlyyyyn]

Here's the extra credit question on my homework:

The number 8 is the sum and product of the numbers in the collection of four positive integers (1,1,2,4) since 1+1+2+4=8 and 1 x 1 x 2 x 4=8. The number 2007 can be made up from a collection of n positive integers that multiply to 2007 and add to 2007. What is the smallest value of n with n>1?

Does that even make sense? And if it does, what's the answer because everyone in my class has absolutely no idea how to solve it

 

[mmm4444bot]

Does that even make sense? And if it does, what's the answer

Yes, it makes sense. It's an excellent question to get you to think.

They reasoned that n must be 4 (i.e., you need at least four factors, to get both their sum and product to equal 8).

You can't have two or three factors. They won't be integers. Try it and see.

But notice that they found two factors (2 and 4) which multiply to make 8 but sum to 6, so they just added enough factors of 1 to get four factors that add up to 8.

1, 1, 2, 4

Were you at all curious about factors of 2007? I mean, did you try to find some, by starting with the Prime Factorization of 2007, perhaps?

That's where I would start.

What do those factors tell you about how may digits you need, in order for the factors to all add up to 2007? In other words, think about how many repeats of the prime factors, other factors, and 1 you need, when considering the smallest n.

Otherwise, tell us what you've done thus far. Cheers

 

[Kaitlyyyyn]

Is the answer 1337? If it isn't please tell me what the real one is, my math teacher even told us himself he hadn't taught us how to do this kind of math yet, he just told us no one has ever answered it correctly before.

 

[Deleted member 4993]

Is the answer 1337? If it isn't please tell me what the real one is, my math teacher even told us himself he hadn't taught us how to do this kind of math yet, he just told us no one has ever answered it correctly before.

Before I say correct or incorrect - tell us

Did you find the prime factors of 2007?

What are those?

Since this is extra credit - you need to work a bit more before we give you the answer.

 

[Denis]

Try an easier one to "see" whadda heck's going on here! Say 60:
3 * 4 * 5 = 60
2 * 3 * 10 = 60
2 * 30 = 60
How many 1's do you need in each case?
That should give you some kind of "hint".

 

[Kaitlyyyyn]

Is the answer 1337? If it isn't please tell me what the real one is, my math teacher even told us himself he hadn't taught us how to do this kind of math yet, he just told us no one has ever answered it correctly before.

Before I say correct or incorrect - tell us

Did you find the prime factors of 2007?

What are those?

Since this is extra credit - you need to work a bit more before we give you the answer.

Aren't the prime factors 3, 3, 223?

 

[Deleted member 4993]

Aren't the prime factors 3, 3, 223?

Yes ... then following Denis's example - which combination will give you highest "additive" value?

How many more 1's would you need to add up to 2007?