奧數題解答

Let a1 , a2 , ... , a7 be the seven numbers

if d is a common factor of these 7 numbers

then d divide each number a1 , ... , a7 and hence divide their sum
2008

Also, since d is a factor
we know that d <= a1 , d<=a2 , ... , d<=a7

First we find out the factor of 2008

2008 , 1004 , 502 , 251 , 1
are the 5 possible factor

since every number a1 , a2 , ... , a7 >=d
we must have the sum of them
a1 + a2 + ... + a7 >= 7d
the largest number such that 7d is not greater than 2008 is 251
so the answer is 251

因有7個數,明顯這個公因數小於2008/7=286,2008=8x251,所以251

2009-01-03 13:00:41 補充：
是最接近,
7個數就是6個251和1個251x2=502

2009-01-03 13:08:17 補充：
(當七個數公因數最大時)