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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?

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

Pattern Snake

Stage: 3 Short Challenge Level: Challenge Level:1

2004 is a multiple of 3 (since the sum is a multiple of 3) and also a multiple of 4 (since the last two digits form a multiple of 4). So 2004 is a multiple of 12 and hence the part of the pattern between 2007 and 2011 is the same as the part between 3 and 7.

This problem is taken from the UKMT Mathematical Challenges.

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