최대공약수: 두 판 사이의 차이

* (재귀적 정의) <math>\gcd\{\gcd\{\gcd\{\cdots\gcd\{\gcd\{n_1,n_2\},n_3\}\cdots\},n_{k-1}\}n_k\}</math>

 

 

== 성질 ==

:<math>\gcd\left\{\frac nk,\frac mk\right\}=\frac{\gcd\{n,m\}}k\qquad(k\mid n,m)</math>

:<math>\gcd\left\{\frac{n_1}k,\frac{n_2}k,\dots,\frac{n_t}k\right\}=\frac{\gcd\{n_1,n_2,\dots,n_t\}}k\qquad(k\mid n_1,n_2,\dots,n_t)</math>

:<math>\gcd\left\{\frac n{\gcd\{n,m\}},\frac m{\gcd\{n,m\}}\right\}=1</math>

:<math>\gcd\left\{\frac{n_1}{\gcd\{n_1,n_2,\dots,n_t\}},\frac{n_2}{\gcd\{n_1,n_2,\dots,n_t\}},\dots,\frac{n_t}{\gcd\{n_1,n_2,\dots,n_t\}}\right\}=1</math>