标题: 求助 Prep 数学题 一道 [打印本页] 作者: 快乐追逐 时间: 2011-3-22 16:06 标题: 求助 Prep 数学题 一道 The positive integer k has exactly two positive prime factor , 3 and 7 . If k has a total of 6 positive factor, including 1 and k , what is K ? (1) 3^2 is a factor of k (2) 7^2 i s not a factor of k
題目說 , 共6個因子 因此(x+1)(y+1)=6,則共有(2,3)(3.2)-->(x,y) 有 either(1,2)or(2,1) 的組合 所以 , , , 的互相乘積皆是可能factors (1) 32 is a factor of k. (3^0)(7^0) = 1 (3^0)(7^1) = 7 (3^1)(7^0) = 3 (3^1)(7^1) = 21 (3^2)(7^0) = 9 (3^2)(7^1) = 63 (k, itself) (x≧2, so it must be true that x=2 and y=1) 由條件得知k's positive factors:1,3,7,9,21,k k=63 .........sufficient (2) 72 is not a factor of k. k有6個positive factors,且只有3,7兩個質因子 表示k可因式分解為 ×7or 3× 此條件排除了第二個可能,y<2, so x=2 and y=1. 所以k=63 ...............sufficient *************
kai  rep 完整詳解版作者: Rainbeauty 时间: 2011-3-22 18:01
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