5, 3, -6, 8, 1 4, 2

    Walk through elements; switch them if they are out of order.

                        p
    5, 3, -6, 8, 1, 4, 2
    3, 5, -6, 8, 1, 4, 2
    3, -6, 5, 8, 1, 4, 2
    3, -6, 5, 1, 8, 4, 2
    3, -6, 5, 1, 4, 8, 2
    3, -6, 5, 1, 4, 2, 8  (8 bubbled up to the top)
                     p
    3, -6, 5, 1, 4, 2, 8 
    -6, 3, 5, 1, 4, 2, 8  
    -6, 3, 1, 5, 4, 2, 8  
    -6, 3, 1, 4, 5, 2, 8  
    -6, 3, 1, 4, 2, 5, 8  
                  p
    -6, 3, 1, 4, 2, 5, 8  
    -6, 1, 3, 4, 2, 5, 8  
    -6, 1, 3, 2, 4, 5, 8  
               p
    -6, 1, 3, 2, 4, 5, 8  
               p
    -6, 1, 3, 2, 4, 5, 8  
    -6, 1, 2, 3, 4, 5, 8  
            p 
    -6, 1, 2, 3, 4, 5, 8  
         p
    -6, 1, 2, 3, 4, 5, 8  
      p
         p

Suppose we have a list of length n.

first pass: n - 1
secon pass: n- 2
.
.

last pass: 1

total checks:  1 + 2 + 3 + ...  + (n-1)

n*(n-1)/2  = O(n^2).
"Quadratic sort"
Computing a gcd

Suppose a, b, q and r are integers and that

b = a*q + r

then 

gcd(a,b) = gcd(a,r)

>>> a = 7776
>>> b = 1048577
>>> b = 1048576
>>> r = 1048576%7776
>>> r
6592
>>> r = 7776%6592
>>> r
1184
>>> r = 6592%1184
>>> r
672
>>> r = 1184 % 672
>>> r
512
>>> r = 672%512
>>> r
160
>>> r = 512%160
>>> r
32
>>> 160 % 32
0
>>>