Question

if a= bq+r then -
a) GCD(a,b) = GCD(b,r)
b) GCD(a,r)= GCD(b,q)
c) GCD(a,q) = GCD(b,q) d)GCD(q,r)= GCD(b,r)
which one is correct

Answer 1

a = bq + r then, GCD(a, b) = GCD( b, r)
hence, option (A) is correct .

Explanation :-
Let P is the greatest common divisor of and and of b .
it means a = Pm { m is some constant number }
b = Pn { n is some constant number}
Now,
a = bq + r
Pm = Pnq + r
P( m - nq) = r
PK = r { where K = (m-nq)}
Hence, P is also greatest common divisor (GCD) of r .
Hence ,
GCD{a, b} = GCD{ b, r}

Answer 2

Answer:

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