# Definition:Greatest Common Divisor/Also known as

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## Definition

The **greatest common divisor** is often seen abbreviated as **GCD**, **gcd** or **g.c.d.**

Some sources write $\gcd \set {a, b}$ as $\tuple {a, b}$, but this notation can cause confusion with ordered pairs.

The notation $\map \gcd {a, b}$ is frequently seen, but the set notation, although a little more cumbersome, can be argued to be preferable.

The **greatest common divisor** is also known as the **highest common factor**, or **greatest common factor**.

**Highest common factor** when it occurs, is usually abbreviated as **HCF**, **hcf** or **h.c.f.**

It is written $\hcf \set {a, b}$ or $\map \hcf {a, b}$.

The archaic term **greatest common measure** can also be found, mainly in such as Euclid's *The Elements*.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**common factor (common divisor)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**common factor (common divisor)**