Use the Euclidean algorithm to find

a) gcd(1, 5).

b) gcd(100,101).

c) gcd(123, 277).

d) gcd(1529, 14039).

e) gcd( 1529, 14038).

f) gcd( 11111, 111111).

Solution:-

Step1

Given that

We have to use the Euclidean algorithm to find gcd.

Step2

a) gcd(1, 5)

By using Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore, gcd(1, 5) is 1.

Step3

b) gcd(100,101)

By using Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore, gcd(100, 101) is 1.

Step4

c) gcd(123, 277)

By using Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore, gcd(123, 277) is 1.

Step5

d) gcd(1529, 14039)

By using Euclidean algorithm