The Mathematical Symbol "Divides (∣)"

Deep Dive into the "Divides" Symbol (∣): A Fundamental Notion in Number Theory

The world of mathematics thrives on precise symbols that encapsulate specific relationships or operations. Among them, in the domain of number theory and algebra, the "Divides" notation, depicted as ∣, holds considerable significance. This article endeavors to shed light on this symbol, accompanied by illustrative examples.

Dissecting the ∣ Symbol

Essentially, the ∣ symbol indicates a divisibility relationship between two integers. It asserts that one integer is a divisor of another without leaving a remainder. Stated differently, if \( a \) and \( b \) are integers and \( a \mid b \), then there exists an integer \( c \) such that \( b = a \times c \).

Example 1:

Consider the numbers 4 and 12. Since 4 divides 12 evenly, with 12 being \( 4 \times 3 \), we can depict this relationship as:

4 ∣ 12

Example 2:

Given the numbers 5 and 25, it's evident that 5 is a divisor of 25, with 25 being \( 5 \times 5 \). Thus, the notation becomes:

5 ∣ 25

The ∣ notation is foundational in various branches of mathematics, especially number theory and abstract algebra. It provides a concise way to express divisibility, a concept pivotal in discussions about prime numbers, factorization, and numerous other topics. Recognizing and understanding this symbol is crucial for anyone delving into advanced mathematical studies.

Mathematical symbol 'Divides'

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Codes for the ∣ Symbol

The Symbol
Alt CodeAlt 8739
HTML Code∣
HTML Entity∣
CSS Code\2223
Hex Code∣

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 8739. 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: &#8739;</b>My symbol: ∣

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

HTML TextOutput
<b>My symbol: &mid;</b>My symbol: ∣

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

CSS and HTML TextOutput
span:after {
content: "\2223";}
<span>My symbol:</span>
My symbol: ∣

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

HTML TextOutput
<b>My symbol: &#x2223;</b>My symbol: ∣
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2223 to place the ∣ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

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

The Unicode for ∣ is U+2223. 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:
[Hold down Alt]
[Press x]

(The 2223 turns into ∣. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2223. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2223"
document.write("My symbol: " + str)
My symbol: ∣