indivisible

Indivisible is an adjective meaning not divided or incapable of being divided into smaller parts. In everyday use it can describe a solid, unified whole or a concept regarded as a single unit.

In mathematics, indivisible often refers to a quantity that cannot be expressed as a product of two nontrivial factors. In elementary number theory, the positive integers greater than 1 that have no positive divisors other than 1 and themselves are prime; such numbers are indivisible by any other number besides 1 and themselves. In more advanced algebra, related ideas appear as irreducible or prime elements in rings, where irreducible elements cannot be factored into smaller non-unit elements, though the precise relationships between irreducible and prime vary by mathematical setting.

Etymology traces the word to Latin indivisibilis, meaning not divisible. The term historically echoes the ancient Greek concept of atoms, from a root meaning indivisible, a notion later revised by discoveries showing subatomic structure.

In political and cultural contexts, indivisible is used to express unity. A well-known example is the phrase one nation, indivisible, which appears in national pledges and oaths and is invoked to emphasize cohesion within a state or polity.

Beyond formal use, indivisible can describe any unit or idea treated as a single, inseparable whole, such as indivisible rights, commitments, or components that are considered inextricable from the system they constitute.