You may also like

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Factor Sum

Age 11 to 14 Short
Challenge Level

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 $15$
So only $5$ is impossible.


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.