### 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?

### Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

# Weekly Problem 17 - 2010

##### 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.

View the previous week's solution
View the current weekly problem