Consecutive Numbers

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

14 Divisors

What is the smallest number with exactly 14 divisors?

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

If the first two digits are $a$ and $b$ (with $a\neq 0$) then the six terms will be $a$, $b$, $a+b$, $a+2b$, $2a+3b$ and $3a+5b$, so we must have $3a+5b \leq 9$.
If $b=0$ then $a$ can be $1$, $2$ or $3$. If $b=1$ then $a$ can only be $1$, and $b$ cannot be greater than $2$.
Hence there are four possibilities, namely $101123$, $202246$, $303369$ and $112358$.