The Mathematical Symbol "Does Not Divide (∤)"

The "Does Not Divide" Symbol (∤): Breaking It Down

The "Does Not Divide" notation, symbolized as ∤ is a mathematical symbol used predominantly in number theory and algebra. It indicates a specific non-relation between two numbers: one number does not divide another without leaving a remainder. In this article, we'll explore this concept further and provide two illustrative examples.

Concept in Number Theory and Algebra

In mathematics, especially in number theory and algebra, the ∤ symbol is used to state that one number, say \(a\), does not divide another number, \(b\), exactly. In other words, when \(b\) is divided by \(a\), there is a non-zero remainder.

Example 1:

Considering the numbers 3 and 7:

3 does not divide 7 without leaving a remainder. Hence, we can write 3 ∤ 7.

Example 2:

Looking at the numbers 4 and 10:

While 4 does divide 12 with no remainder (resulting in 3), it does not divide 10 without a remainder. Therefore, we can represent this as 4 ∤ 10.

Through these examples, the utility of the "Does Not Divide" notation in expressing a specific relationship between numbers becomes evident. As with most mathematical symbols, it's imperative to understand the context to interpret its exact meaning accurately.

Mathematical symbol 'Does Not Divide'

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Codes for the ∤ Symbol

The Symbol∤
Alt CodeAlt 8740
HTML Code∤
HTML Entity∤
CSS Code\2224
Hex Code∤
UnicodeU+2224

How To Insert the ∤ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∤ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8740. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8740;</b>My symbol: ∤

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &nmid;</b>My symbol: ∤

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
<style>
span:after {
content: "\2224";}
</style>
<span>My symbol:</span> 		My symbol: ∤

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x2224;</b>My symbol: ∤
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2224 to place the ∤ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

∤

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∤ is U+2224. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
2224
[Hold down Alt]
[Press x]		∤
(The 2224 turns into ∤. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2224. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2224"
document.write("My symbol: " + str)		My symbol: ∤