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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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14 Divisors

What is the smallest number with exactly 14 divisors?

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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?

Adjacent Factors

Stage: 3 Short Challenge Level: Challenge Level:1

Peter wishes to write down a list of different positive integers less than or equal to 10 in such a way that for each pair of adjacent numbers one of the numbers is divisible by the other. 
 
What is the length of the longest list that Peter could write down?
 

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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