English Question

中文意思

「30 和 45 的公因數 (即共同因數) 是否是 30 和 45 的最大公因數的因數﹖」

30 的因數是：3, 5, 6, 10, 15
45 的因數是： 3, 5, 9, 15
30 和 45 的公因數是 3, 5, 15, 15 是最大公因數。

3, 5, 15 當然是也是 15 的因數。

2012-09-12 23:12:32 補充：
30 的因數是：2, 3, 5, 6, 10, 15

2012-09-14 00:36:41 補充：
Thanks, Godfrey, for your correction.

Two or more numbers are both divisible by their common factors including the highest common factor. Being the highest, the HCF is divisible by all the common factors including itself.

30 的因數是：1, 3, 5, 6, 10, 15, 30 (包括1, 30), 30 = 1 x 30
45 的因數是： 1, 3, 5, 9, 15, 45 (包括 1, 45), 45 = 1 x 45
30 和 45 的公因數是 3, 5, 15
15 是最大公因數

Factor = 因數
Common Factor = 公因數
Highest Comon Factor = 最大公因數

(mathematics):-a number that divides into another number exactly:-3 and 5 are the common factors of 30 , 45 (both in common)
Also the h.c.f.=3x5 are the h.c.f. of 30 , 45 (both once the highest in common)
Hence the parts(3 , 5) are to be included in largest part of (3x5).