Factor sum
Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?
Age
11 to 14
Challenge level
Problem
Given any positive integer $n$, Paul adds together the distinct factors of $n$, other than $n$ itself.
Which of the numbers $1$, $3$, $5$, $7$ and $9$ can never be Paul's answer?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 5
- $1:$ yes, all primes
- $3=1+2$ e.g. $4$
- $5=1+4$ impossible as if $4$ is a factor then $2$ is as well
$5=1+2+2,1+1+3$ no other possible ways. - $7=1+2+4$ e.g. $8$
- $9:1+2+5=8$, $1+2+7=10$, $1+3+5=9$ and $1,3,5$ are factors of $15$