Divisibility by 6

Theorem

An integer $N$ expressed in decimal notation is divisible by $6$ if and only if

$N$ is even

and:

$N$ is divisible by $3$.


Proof

We have that:

$6 \divides N \iff 2 \divides N \land 3 \divides N$

The result follows by definition of even integer.

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): divisible
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divisible
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