## Scenario

Here's a Problem to Ponder that will help your students ease back into the groove at the start of the school year. Students usually know that prime numbers have exactly two factors -1 and the number itself. But, which numbers have exactly three factors? Exactly four factors? Exactly five factors? Exactly six factors?

The general extension: Given a positive integer,
*n*
, how can we tell exactly how many factors it has?

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#### Source

Problems to Ponder, August 2011