All natural numbers can be written as the product of two natural numbers. Prime numbers can be written as the product of 1 and themselves. Composites can be written in more than one way as a product of two natural numbers. For instance,

So 12 can be written as the product of two natural numbers in 3 distinct ways.

(

*Note*: We consider and to be the same product pair.)

What is the smallest

*odd*number which can be factored into the product of two natural numbers in exactly 40 different ways? And what about the smallest

*even*number?