If \(n\) is even, \(n\) is divisible by 2.

February 22, 2026

$If \(n\) is even, \(n\) is divisible by 2.$

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5**Question:** What is the largest integer that must divide the product of any three consecutive integers?
Let the three consecutive integers be \(n\), \(n+1\), and \(n+2\). The product is \(n(n+1)(n+2)\). Among any three consecutive integers, at least one is divisible by 2 and at least one is divisible by 3. Therefore, the product is divisible by \(2 \times 3 = 6\).
To see if a larger number must divide the product, consider the following cases:
If \(n+1\) is even, then \(n+1\) is divisible by 2.
If \(n+2\) is even, then \(n+2\) is divisible by 2.
In each case, there is at least one factor of 2.

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