Question

If d divides a and d divides b, prove that d divides gcd(a,b).

Answer 1

Answer:

GCD(a,b) is multiple of d. It means d divides GCD(a,b).

Step-by-step explanation:

Let a and b are two unknown numbers.

If d divides a and d divides b, then a and b are multiple of d.

$a=d\cdot m=dm$

$b=d\cdot n=dn$

where, m and n are integers.

The greatest common divisor of a and b is

$GCD(a,b)=d\cdot m\cdot n$

$GCD(a,b)=d\cdot mn$

GCD(a,b) is multiple of d. It means d divides GCD(a,b).

Hence proved.