# irreducible

> English word · Adjective · IPA /ˌɪɹɪˈdjuːsɪbəl/ · frequency rank #42,213

## Definitions
1. Not able to be reduced or lessened.
2. Not able to be brought to a simpler or reduced form.
3. Unable to be factorized into polynomials of lower degree, as (x² + 1).
4. Whose numerator and denominator share no common factor greater than 1.
5. Unable to be factored into smaller integers; prime.
6. Whose only divisors are units and associates.
7. Inexpressible as the union of two proper algebraic subvarieties.
8. Not containing a sphere of codimension 1 that is not the boundary of a ball.
9. Impossible to divide further into representations of lower dimension by means of any similarity transformation.

## Etymology
From ir- + reducible.

## Common misspellings (15)
`ireducible`, `irerducible`, `irrdeucible`, `irredcuible`, `irredducible`, `irreducable`, `irreducbile`, `irreduccible`, `irreducibble`, `irreducibel`, `irreduciblle`, `irreducilbe`, `irreduicble`, `irreudcible`, `rireducible`

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/irreducible