SOLUTION: "Show that the product of three consecutive natural numbers is divisible by 6"

SOLUTION: "Show that the product of three consecutive natural numbers is divisible by 6"

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Question 451601: "Show that the product of three consecutive natural numbers is divisible by 6"
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For any three consecutive natural numbers, at least one of them will be divisible by 2, and exactly one will be divisible by 3 (using modular arithmetic, the integers are 0,1,2; 1,2,0; or 2,0,1 mod 3). This implies that the product must be divisible by 6.
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