Please provide proofs of each of the following If da can it

Please provide proofs of each of the following.

If d|a, can it be that d > 2? Suppose a and b are even. Show that gcd(a, b) > 1.

18.6)

If d|a,can it be that d>a/2

Yes, it is possible only for the case when d=a

Otherwise, it is impossible that d divides a and d > a/2

18.7)

Since both a and b are even, then we can write

a = 2k1, where k1 is an integer

b = 2k2, where k2 is an integer

gcd(2k1,2k2)

Case 1: If k1 and k2 don\'t have any common factors then

gcd(2k1,2k2) = 2, which is greater than 1

Case 2: If k1 and k2 have a common factor let us suppose p1

then gcd(2k1,2k2) is equla to 2p1, which is also greater than 1

Hence for both the cases, gcd(a,b) > 1