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).
最大公約数を求める。
To find the greatest common divisor.
12と18の公約数は1、2、3、6だ。
The common divisors of 12 and 18 are 1, 2, 3, and 6.
分数を約分するときは公約数で割る。
When reducing a fraction, you divide by a 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.
両チームの最大公約数となる意見を探した。
We searched for the opinion that would serve as the greatest common ground between the two teams.
この提案は社内の様々な意見の最大公約数として採用された。
This proposal was adopted as the common ground shared by various opinions within the company.
多様な価値観を持つメンバーの最大公約数を見つけ出すのは簡単ではない。
It is not easy to find the greatest common ground among members with diverse values.
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 TERMS:
- 約数: divisor, factor — numbers that divide evenly into a given number
- 公倍数: common multiple — the counterpart of 公約数
- 最小公倍数: least common multiple (LCM)
- 約分: reduction of a fraction — the main practical use of common divisors
- 共通点: common point / shared trait — more general word for figurative commonalities