### 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?

# Factorised Factorial

##### Stage: 3 Short Challenge Level:
$n!$ is divisible by $5^3$ so $n!$ must be at least $15$. But $15!$ is only divisible by $2^{11}$ so $n$ is not $15$. $n!$ is not divisible by $17$ so $n$ is less than $17$. Hence $n=16$.

This problem is taken from the UKMT Mathematical Challenges.
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