Let abcd and e be integers with a not equal to 0 If gcdabace

Let a,b,c,d, and e be integers with a not equal to 0. If gcd(ab,ac)=e and gcd(b,c)=d, then e divides ad. Please answer in correct proof written form.

Solution

Given that a,b,c,d and e are integers non zero.

ab and ac have greatest common factor =e.

Since a is one common factor, we have e/a is the gcf between b and c.

Since b and c have common factor d, we get e/a =d

Or e = ad

i.e. e divides ad.