### 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?

### Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

# Circle Time

##### Stage: 3 Short Challenge Level:

Three circles $C_1$, $C_2$ and $C_3$, of radii 1 cm, 2 cm and 3 cm respectively touch as shown. $C_1$ meets $C_2$ at $P$ and meets $C_3$ at $Q$.

What is the length in cm of the longer arc of circle $C_1$ between $P$ and $Q$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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