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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, ¿ìè¶ÌÊÓƵ, 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