Paul takes a natural number n and adds together the distinct factors of n other than n itself. Which of these numbers can never be Paul's answer.

A. 1 B. 3 C. 5 D. 7 E. 9
(I saw this problem in a maths challenge exam and I assume that distinct factors mean all factors including 1 and n)

Question

Paul takes a natural number n and adds together the distinct factors of n other than n itself. Which of these numbers can never be Paul's answer.

A. 1     B. 3     C. 5     D. 7     E. 9
(I saw this problem in a maths challenge exam and I assume that distinct factors mean all factors including 1 and n)

anonymous · Answer

1 because it doesn't have any factors other than itself and 3, 5, 7 because they're prime.

anonymous · Answer

if you want a guess i will guess 9

anonymous · Answer

1 works because 1 is a natural number and its factors are just one and itself.  not counting itself and adding we get 1

anonymous · Answer

no thats not the answer bendt - they are looking for the ANSWER of the addition. for example  if you take number 4  factors are 1 2 which add up t 3 (B)

anonymous · Answer

i think the answer is 5

anonymous · Answer

oops maybe it is 3.  the factors would have to be 1 and 2 yes?

anonymous · Answer

no - 3 is possible

anonymous · Answer

it says adds together the distinct factors of n other than n itself" not the number of factors

anonymous · Answer

hmm - i'm more confused now!

anonymous · Answer

i'm tempted to check the right answer - i have them here but not looked yet

anonymous · Answer

is my definition of distinct factors corredt

anonymous · Answer

the way i look at it is if my definition of distinct factors is correct then 3 cannot be the answer because  for 4  they are 1 2 and 4 so the addition is 1 + 2 = 3.

anonymous · Answer

i've googled distinct factors without success

anonymous · Answer

they have used the definition i assumed.
if we take n = 2  factors- 1,2 -  addition gives  1
  n =3 -   factors 1,3 - addition = 1
 n = 4- factors 1,2,4  addition = 3 
n=5 - factors 1,5 addition = 1
n=6 - factors 1,2,3,6 addition = 6
n=7 - factors 1,7 addition = 1
n=8 - factors 1,2,4,8 addition = 7
n=9 - factors 1,3,9 addition = 4
n=10 - factors 1,2,5,10 addition = 8
n = 11  gives
n=12 factors 1,2,3,4,6,12 addition = 16
n=13 give 1
n=14 factors = 1,2,7,14 addition = 10
n=15 factors = 1,3,5,15 addition = 9

so the answer is C.5

I thought it was 5 but to be honest it was a guess
There's more to this question than meets the eye - its quite tricky.

anonymous · Answer

i gave up up on this one and had to check the answer!!