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Déjà vu

I have in mind a number N. I’ll tell you some things about it:

It is more than 2. If you draw a figure with that number of straight sides, with all its angles the same and with all the vertices lying on a circle, then all the sides will be equal in length. And the angles will be whole numbers of degrees.

And how many of the numbers 1, 2, 3,… , N divide exactly into N? I’ve worked out that number and I’ll tell you something about it:

It is more than 2. If you draw a figure with that number of straight sides, with all its angles the same, and with all the vertices lying on a circle, then all the sides will be equal in length. And the angles will be whole numbers of degrees.

What is N?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 21 April. The Editor’s decision is final. Please send entries to Enigma 1587, New ÐÓ°ÉÔ­´´, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1581 Daley’s Gold: The number is 103274

The winner Simon Scarle, Nuneaton, Warwickshire, UK