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?

Weekly Problem 47 - 2010

Stage: 3 Short Challenge Level:

The difference between $\frac{1}{3}$ and $\frac{1}{5}$ is $\frac{1}{3}-\frac{1}{5}= \frac{2}{15}$.

This section of the number line is divided into $16$ intervals, each of length $\frac{2}{15}\div 16 = \frac{1}{120}$.

The difference between $\frac{1}{4}$ and $\frac{1}{5}$ is $\frac{1}{4}-\frac{1}{5}= \frac{1}{20}= \frac{6}{120}$, and hence $\frac{1}{4}$is six smaller intervals from $\frac{1}{5}$.

This problem is taken from the UKMT Mathematical Challenges.

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