### 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 48 - 2010

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

When Tina chose a number N and wrote down all of its factors, apart from $1$ and N, she noticed that the largest of the factors in the list was $45$ times the smallest factor in the list. How many numbers N could Tina have chosen for which this is the case?

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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