Divides and Does Not Divide in LaTeX

Write "a divides b" as a \mid b and "a does not divide b" as a \nmid b (from amssymb, which most templates load). Do not use the keyboard |: it is an ordinary symbol, so a | b has no space around the bar.

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Divisibility symbols

a \mid b
$a ∣ b$
a divides b. A relation, with space on both sides.
a \nmid b
$a ∤ b$
a does not divide b (amssymb).
a \not\mid b
$a ∤ b$
Fallback without amssymb; the slash may sit a little off.
p^k \parallel n
$p^{k} ∥ n$
p^k exactly divides n (some authors use ∥ for this).
\{\, x \mid x > 0 \,\}
${x ∣ x > 0}$
\mid is also the "such that" bar in set-builder notation.

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LaTeX

Templates

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Divides and does not divide examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Divides
$3 ∣ 12$
LaTeX
```
3 \mid 12
```
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Does not divide
$5 ∤ 12$
LaTeX
```
5 \nmid 12
```
Edit here Open in editor
Common divisor
$d ∣ a and d ∣ b ⟹ d ∣ gcd (a, b)$
LaTeX
```
d \mid a \;\text{and}\; d \mid b \implies d \mid \gcd(a, b)
```
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Prime divisor
$p ∣ a b ⟹ p ∣ a or p ∣ b$
LaTeX
```
p \mid ab \implies p \mid a \;\text{or}\; p \mid b
```
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Divisibility by a power
$2^{k} ∣ n but 2^{k + 1} ∤ n$
LaTeX
```
2^k \mid n \quad\text{but}\quad 2^{k+1} \nmid n
```
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\mid, | and \vert

All three draw a vertical bar, but with different spacing. \mid is a relation, like =, so it gets a thick space on each side. | and \vert are ordinary symbols with no added space, right for absolute values |x| and norms, wrong for divisibility.

In set-builder notation \{ x \mid x > 0 \} the relation spacing of \mid is also what you want. For a bar that grows with tall content, use \middle| between \left\{ and \right\}.

Negating the symbol

\nmid is a single, well-designed glyph from amssymb. \not\mid overlays a slash on \mid and works without packages, but the slash can look misplaced in some fonts.

Common mistakes

The keyboard bar is an ordinary symbol, so the letters touch it.
Instead of
```
a | b
```
Write
```
a \mid b
```
Without amssymb \nmid is undefined; load it or use \not\mid.
Instead of
```
a \nmid b  (no amssymb)
```
Write
```
\usepackage{amssymb}
```
Divisibility is a vertical bar, not a slash.
Instead of
```
a \backslash b
```
Write
```
a \mid b
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\mid works everywhere; \nmid needs amssymb (loaded by most templates).
MathJax and KaTeX
MathJax and KaTeX support \mid, \nmid and \not\mid without configuration.
Microsoft Word
In a Word equation \mid followed by Space inserts ∣; \nmid gives ∤.

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