How we can find G.C.M of 2541 and 3102 in scale of 7 ?

Answer 1

Are we talking Base 7 here?
If so:-
343---49---7---1
--2-----5---4----1 = 960 in base ten
--3-----1----0---2 = 1080 in base ten
960 = 10 x 96
960 = 2 x 5 x 12 x 8
960 = 2 x 5 x 3 x 2² x 2³
960 = 2^(6) x 3 x 5
1080 = 10 x 4 x 27
1080 = 2³ x 3³ x 5
Highest common factor is 2^3 x 3 x 5 = 120
In base 7 this becomes 231

Answer 2

2541/7 = 363 and 3102/7 = 443 1/7

The second number is not divisible by 7. Hence the GCM of the two numbers is 7 X 363 X 3102