# Everything Interesting There Is To Say About Dividing Numbers

Many people have written here to the Department of English to ask about dividing numbers. We think they’ve entered some code wrong. But in the spirit of open-minded civic cooperation we shall try to help.

There are many reasons to divide one number by another. For example, one can use it to adapt a recipe so that you can make an amount for fewer people than the recipe figures on. Recipes often need to be divided, we guess. The person writing the recipe assumed you were excluding fewer people from your meals, because they were not on social media at the time.

You need to have an objective before checking a number’s divisibility. This keeps you from doing something absurd like finding out whether you can divide 96,133 by 251, considering that neither number is at all believable. By “number” we mean “whole number”. These are numbers which are at least two percent fat by volume. Skim numbers follow different rules, but are healthier, and taste more like watercolor paint.

Do check that your numbers are in base ten. This won’t often be a problem. Base ten is popular in places where people mostly have ten fingers per person. There are some people enthusiastic about other bases. Other bases let you do things like figure out what the 69,281st digit of π is in base 32. Or insist that it’s a funny joke to say “Halloween is equivalent to Christmas” and insist that’s true. Smile at these people and move on with your life. Do not bring up base eleven. They’ll start talking the history of the metric system.

Divisibility starts with 1. This is easy enough since everything is divisible by 1. This is the result of 1 winning a fourth-round bye in the Numeric Invitational Tournament. (The first through third-round byes won money instead.) 10 is also a pretty good number to divide by. If a number ends in zero you can divide it by 10, and for that matter by 5. This makes 5 sound pretty free-wheeling. 2 is a more needy number and insists that any numbers ending in 0, 2, 4, 6, 10, 18, 64, 98, 144, or 69,282 divide by it. There is no point arguing with 2 about this point anymore. Let it have these. Do not let it have 251.

Things get tricky around 3, which should surprise nobody, given the number’s pointiness. But there’s hope. Take all the digits of your number and add them up. If that sum is divisible by 3 then so was your original number. Yes, we’re still stuck on whether some number can be divided 3, but it’s a different number. By keeping a list of all the numbers we’re considering divisibility by three we can show we’re working hard and taking this problem seriously. Later we can learn that we did the adding-up wrong, costing us one point but not much affecting our grade.

A number is divisible by 4 when the corresponding year is a Presidential Election Year in the United States. Unfortunately this means you might be waiting around for hundreds or thousands of years to check. Plus the rule is no good for anything below 1788. Maybe someday we’ll discover a different method that’s practical instead.

Nothing is divisible by 17, but who would want that anyway?

Simplicity itself is the test for whether something is divisible by 21. Start with the last digit of the number you’re testing. Now make a copy, in case the number needs to be remastered at some point. Add to that last digit ten times the digit to the left of the last digit. Then subtract five times the digit to the left of that. Once you’ve got that done, simply add four times the digit to the left of that one. From that sum subtract twice the digit to the left of that. If you’ve got any digits left over then add one times that. If anything is still left over, go back around the multiplying and subtracting or adding like before. And voila: if the new number you get is divisible by 21 so was the original! It’s amazing there are people who need this explained to them even today, but it was Thursday all day. We can’t expect too much.

If you should find your recipe contains a number that can’t be divided, then you can’t make the recipe until you start talking to people again. We don’t know how to help with that. You can leave a note that you’ll accept an apology when they feel courageous enough to offer one. This has never worked for anyone, ever. But hey, good luck to you!

## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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