請幫我解釋，步驟及列式

Let k cm x kcm be the size of the square.
If the squares can exactly cover the rectangle,

k is a factor of 36.
k is also a factor of 84.

For the largest k,
k is the Highest Commom Factor(HCF) of 36 and 84.

Factors of 36:
1, 2, 3, 4, "6", 9, 12, 18, 36

Factors of 84:
1, 2, 3, 4, "6", 7, 12, 14, 21, 28, 42, 84

So, the Highest Commom Factor(HCF) of 36 and 84 is 6.
k=6

The largest size of the squares are 6 cm x 6cm.

2009-08-13 11:20:52 補充：
Very sorry, mistake correction:

The Highest Commom Factor(HCF) of 36 and 84 is 12.
k=12

The largest size of the squares are 12 cm x 12cm.

2009-08-13 11:21:24 補充：
k is 12, NOT 6

2009-08-13 11:48:38 補充：
Actaully, if the question is transform into this:

"A rectangle 0.36m by 0.84m is to be covered with squares which are of the same size .Find the largest size of the squares that can be used to exactly cover the rectangle."

2009-08-13 11:48:54 補充：
The question is the same, but you cannot use HCF becasue 0.36 and 0.84 are not integers!!!!

So, you can do the question in another way:

2009-08-13 11:49:18 補充：
Let t m x t m be the size of the square.
If the squares can exactly cover the rectangle,
0.36 = tn, where n is a positive integer.
0.84 = tm, where m is another positive integer.

2009-08-13 11:49:38 補充：
So,
0.36　　tn
------- = --------
0.84　　tm

0.36　　 n
------- = -------
0.84　　 m

36　　 n
----- = -------
84　　 m

3　　 n
---- = -------
7　　 m

n:m =3:7

2009-08-13 11:50:01 補充：
For the largest k, n and m are the smallest.
So, n=2, m=7
t = 0.36/n = 0.36/1=2 = 0.12
OR
t = 0.84/m =0.84/7 =0.12

So, the largest size of the squares are 0.12 m x 0.12m.. i.e. 12cm x 12cm

2009-08-13 11:51:07 補充：
Sorry, mistake correction:
For the largest k, n and m are the smallest.
So, n=3, m=7
t = 0.36/n = 0.36/3= 0.12
OR
t = 0.84/m =0.84/7 =0.12

So, the largest size of the squares are 0.12 m x 0.12m.. i.e. 12cm x 12cm