# Factors and the Lamp Riddle

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Common Core State Standards
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This worksheet has a fill-in-the-blank word bank for integer, factor, composite number, prime number, and perfect square. Then students list the factors for 1-16 and use the vocabulary words. Then students use the table to solve the following riddle.

Riddle: There is a hallway with 16 lamps. A child walks through the hallway. She pulls the chain on each lamp, turning the lamps on. Another child walks through the hallway. He pulls every 2nd chain, turning the lamps off. A third child walks through the hallway. She pulls every 3rd chain, turning some lamps on and turning some lamps off. And so on, until the last child walks through the hallway, pulling only the 16th chain. Which lamps are left on in the hallway? Why?

An illustration of the riddle is included. Square number lamps (1,4,9,16) are left on because they have an odd number of factors. This riddle can be solved for any number of lamps.

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