Why does 3600÷6 have the same quotient as 1800÷3?

Think of it this way:

3600 divided by 2 is 1800
and 6 divided by 2 is 3.

Since both the dividend and the divisor were divided by 2, the quotient is the same for both because the ratios were the same.

3600 = 1800
   6           3
cross multiply
10,800=10,800

The quotients are the same (600).