Use the Euclidean algorithm to calculate gcd832144 Show each

Use the Euclidean algorithm to calculate gcd(832,144). Show each step in the reduction until you get to the final end step as shown in the notes. Do not stop when you can guess the answer.

Solution

832=144*6-32   , 32=144*6-832

144=32*4+16   , 16=144-32*6=144-6*(144*6-832)=-5*144+6*832

32=16*2 +0 . Euclid Algorithm ends

HEnce, 16=gcd(832,144)