Question

One table at a bake sale has 75 oatmeal cookies. Another table has 60 lemon cupcakes. Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?

Answer 1

75 = 3·5², so has 6 divisors. 6 rectangles are possible if you make the distinction between 1×75 and 75×1.

60 = 2²·3·5, so has 12 divisors. 12 rectangles are possible under the same conditions.

The cupcake table can be arranged more ways.

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When 1 is added to each exponent of the prime factors, the product of those sums is the number of divisors. For 75: (1+1)(1+2) = 6; for 60: (1+2)(1+1)(1+1) = 12.