Explain why the product of any three consecutive integers is divisible by 6.

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- Mar 26th 2009, 07:58 PMdoodle08Consecutive integers help. Anyone?
Explain why the product of any three consecutive integers is divisible by 6.

- Mar 26th 2009, 08:46 PMjstew
Well, every other number is divisible by two, and every third number is divisible by three, so at least one of the numbers is divisible by two and at least one is divisible by three. Then clearly the product is divisible by two and divisible by three, or equivalently, divisible by six.