If
a = bq + r
then
¡) G.C.D (a,b) = G.C.D (b,b)
¡¡) G.C.D (a,b) = G.C.D (b,r)
¡¡¡) G.C.D (a,b) = G.C.D (a,r)
¡v) G.C.D (a,b) = G.C.D (q,a)
a = bq + r
then
¡) G.C.D (a,b) = G.C.D (b,b)
¡¡) G.C.D (a,b) = G.C.D (b,r)
¡¡¡) G.C.D (a,b) = G.C.D (a,r)
¡v) G.C.D (a,b) = G.C.D (q,a)
Answers & Comments
Verified answer
answer - the right answer is option (2)
If a = bq + r, then GCD(a, b) = GCD(b, r). P. We will show that if a = bq + r, then an integer d is a common divisor of a and b if, and only if, d is a common divisor of b and r. Let d be a common divisor of a and b.