Problem 25E

Use the Euclidean algorithm to find the greatest common divisor of 10,223 and 33,341.

Solution:

Step1

To find

We have to find the greatest common divisor of 10,223 and 33,341 using the Euclidean algorithm.

Step2

Given that

10,223 and 33,341

By using the Euclidean algorithm( The Euclidean algorithm, is a productive technique for figuring the best regular divisor(GCD) of two numbers, the biggest number that partitions them two without leaving a remainder.It depends on the rule that the best normal divisor of two numbers does not change if the bigger number is supplanted by its distinction with the more modest number.

)

Here Divisor=10223

Dividend=33341

10223=

=

2207=

465=

347=

118=

111=

7=

6=

Therefore, the greatest common divisor of 10,223 and 33,341 using the Euclidean algorithm is 1.