Divisible by 4 and 8

How do you know if a very large number is evenly divisible by 4?

Easy.

The last two digits of the very large number must be divisible by 4. If so, the entire number is evenly divisible by 4.


Let’s look at an example. Oh, say,

5,177,848

That’s evenly divisible by 4 because 48 is evenly divisible by 4. That’s all you need to know. (The full answer is 1,294,462.)

Why?

Here’s the rationale. The next place to the left from 48 in that original number is the hundreds tally. The 8 is the ones place, and the 4 is the tens place, and, in this case, the original number has 8 hundreds. A hundred is always evenly divisible by 4, and, ergo, any multiple of a hundred is evenly divisible by 4.

How do you know if a very large number is evenly divisible by 8?

By the same reckoning you can figure this out. Now, a hundred isn’t evenly divisible by 8, but a thousand is. 1,000 divided by 8 is 125. So, any multiple of 1,000 is evenly divisible by 8. All you need to worry about is the last three digits in your very large number.

In the case of our example above, 848 is evenly divisible by 8 (the answer’s 106). Aiiiiirggggo, the example is completely evenly divisible by 8. (That answer is 647,231.)

Yes!