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Nov 16, 2022

Welcome to Mathnasium’s Math Tricks, series. Today we are determining whether a number can be divided by a power of 2.

Recall that a number is a power of 2 if it can be expressed in the form 2n. For example, 64 is a power of 2 since it can be expressed as 26: 64 = 2 x 2 x 2 x 2 x 2 x 2.

A number is divisible by a power of 2 if *the last “power”-amount of digits can be divided by the power of 2.*

Follow the example below to determine whether the number is divisible by the power of 2.

Step 1: Determine the power of 2.

16 = 24

Step 2: Check whether the last “power”-amount of digits can be divided by the power of 2.

Since 16 is the *fourth* power of 2, we check whether the last *four* digits of 41,328 can be divided by 16.

1,328 is divisible by 16 since it is divisible by 2, four times:

1,328 ÷ 2 = 664

664 ÷ 2 = 332

332 ÷ 2 = 166

166 ÷ 2 = 83

Answer: Yes.

Now, with this strategy, you are ready to determine if any number is divisible by a power of 2. Click here for more practice problems, then check your answers here.

If you missed this, or any of our other Math Tricks videos, check them out on our YouTube channel!

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