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( 08年清华附中考题)如果将八个数 14, 30, 33, 35, 39, 75, 143, 169平均分成两组,使得这两组数的乘积相等,那么分组的情况是什么?
【答案】 30,33,35,169和 14,39,75,143.
【解析】分解质因数,找出质因数再分开
14= 2× 7;
30= 2× 3× 5;
33= 3× 11;
35= 5× 7;
39= 3× 13;
75= 3× 5× 5;
143= 11× 13;
169= 13× 13.
( 1) 30× 33× 35× 169
=( 2× 3× 5)×( 3× 11)×( 5× 7)×( 13× 13)
= 2× 3× 3× 5× 5× 7× 11× 13× 13.
( 2) 14× 39× 75× 143
=( 2× 7)×( 3× 13)×( 3× 5× 5)×( 11× 13)
= 2× 3× 3× 5× 5× 7× 11× 13× 13.
所以分组为 30,33,35,169和 14,39,75,143.