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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

How many regular polygons are there with interior angles that have an integer number of hexadecimal degrees?

The interior angle of a regular polygon with N sides is:

equation

and can be further finessed so as to emphasize an integer part and a fraction.

equation

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For the fraction to represent an integer, N has to be a divisor of 360°.

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The number of divisors (factors) is:

equation

However, not all divisors are usable, since the polygon has to exist. The smallest number of edges a polygon can have is three. Therefore N cannot be 1 or 2.

There are 22 regular polygons with interior angles that have an integer number of hexadecimal degrees.