00:01
We were asked to determine how many divisions are acquired to find the greatest common divisor of the pair 21 -34 using the euclidean algorithm.
00:16
So, recall, the euclidean algorithm starts by dividing the largest integer, which is 34 in this case by the smallest, which is 21.
00:25
Then the divisor is divided by the non -zero remainder until we obtain a remainder of zero.
00:32
And the solution is the last non -zero remainder.
00:35
So we have 34 is equal to 21 times 1 plus 13.
00:47
This is non -zero, so we divide again.
00:51
21 is equal to divided by 13, 13 times 1 plus 8.
00:57
This is a non -zero remainder, so we'll divide 13 by 8.
01:02
This is going to be 8 times 1 plus 5...