Divisibility Tests by Powers of 2

There is a well-known test for divisibility by powers of 2: to check the divisibility of a number M by 2n, we form a new number M' using only the last n digits of M and then examine the divisibility of that number (i.e., M') by 2n. The test works because of the easily-proved fact that M is divisible by 2 if and only if M' is divisible by 2n.

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