Let me write it out all together:

600 = 4 * 136 + 56  ...  136 = 2 * 56 + 24  ...  56 = 2 * 24 + 8  ...  GCF!  ...  24 = 3 * 8 + 0  ...  done!

 

GCF( 600 , 136 ) = 8

 

Let's do a couple more and I won't blather as much!

Use the Euclidean Algorithm to find

GCF( 1725 , 180 )
 

1725 = 9 * 180 + 105  ...  180 = 1 * 105 + 75  ...  105 = 1 * 75 + 30  ...  75 = 2 * 30 + 15  ...  GCF!  ...  30 = 2 * 15 + 0

 

GCF( 1725 , 180 ) = 15