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If it is even, divide it by two. If your second number is also even, your original number is divisible by four. This is a necessary and sufficient condition; A cannot be divisible by four if either of {A, B} is odd.

If either your original number or your second number were odd, then the original number is not divisible by four.

Proof of this rule (by cases):

Where applicable, A = 2B.

  • A even, B even: B = 2m (m is a whole factor of B) and therefore A = 4m, therefore 4 is a factor of A by definition of a factor.
  • A even, B odd: if B is odd, it does not have 2 as a whole factor. Therefore there exists no whole m such that A = 4m, and therefore 4 is not a factor of A by definition of a factor.
  • A odd: A cannot have any even factors. 4 is even. Therefore 4 is not a factor of A.
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