Unitary divisor

In mathematics, a natural number a is a unitary divisor of a number b if a is a divisor of b and if a and ${\displaystyle {\frac {b}{a}}}$ are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and ${\displaystyle {\frac {60}{5}}=12}$ have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and ${\displaystyle {\frac {60}{6}}=10}$ have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number.

Equivalently, a given divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b.

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