In this paper, the question about greatest common factor of Fn and Fn+k is discussed. By using the number theoretic method, the greatest common factor of Fn and Fn+kis given, where n be positive integer, k = 3, 4, 5,6.

• 利用数论方法；进一步探讨了F_n与F_(n+k)的最大公因数；其中n是正整数；k=3；4；5；6.