1.
common divisor; common factor
In mathematics, a positive integer that divides two or more given integers without leaving a remainder. For example, 6 is a common divisor of 12 and 18. The greatest such number is called the 最大公約数 (greatest common divisor).
2.
common ground; common denominator (figurative)
By extension, something shared by multiple parties — a point of agreement, a shared trait, or a common ground. Often used in the phrase 最大公約数 to mean "the greatest common ground" among different people or groups.
We searched for the opinion that would serve as the greatest common ground between the two teams.
This proposal was adopted as the common ground shared by various opinions within the company.
Formed from 公 (common, public) + 約数 (divisor, factor). The mathematical sense is learned in elementary and middle school, and the figurative sense has become a common idiom in business and public discourse.
Usage
- In mathematical contexts, usually paired with 最大 (greatest) as 最大公約数 (GCD). The opposite pairing is 公倍数 (common multiple).
- In figurative usage, almost always in the form 最大公約数 — "the greatest common factor/ground." Used to describe compromises, majority positions, or shared values.
- The figurative sense can carry a slightly negative nuance: a solution that pleases everyone may also be unambitious or bland.
Common collocations
- 最大公約数: greatest common divisor / greatest common ground
- 公約数を求める: to find the common divisor
- 公約数で割る: to divide by a common divisor
- 意見の最大公約数: the common ground among opinions
Related words
Related Words
Related:
約分 (reduction of a fraction)
Related:
共通点 (common point / shared trait)
Related:
倍数 (multiple (of a number))