考慮兩個數$p_1^{k_1}$,$p_2^{k_2}$ 設由他們各自的因子構成的數列為$a_{1i}$與$a_{2i}$,將$b$質因數分解後$p_i$的冪次為$d_i$ 顯然 $gcd(a_{11},a_{12},\ldots,a_{1n})=min(g_1,p_1^{d_1})\\ gcd(a_{21},a_{22},\ldots,a_{2n})=min(g_2,p_2^{d_2})\\ gcd(a_{11},a_{12},\ldots,a_{1n},a_{21},a_{22},\ldots,a_{2n})=1$