For natural numbers, when p is divided by d, the quotient is q and the remainder is r. When q is divided by d’, the quotient is q’ and the remainder is r’. Then if p is divided by dd’, the remainder is

We are given that p on being divided by d given that quotient q and remainder r, giving us the equation
p = qd + r

From the second relation, we can get the second equation to be q = d'q' + r'

Substituting the value of q from the second equation into the first equation, we get p to be (q'd' + r')d + r
p = q'd'd + r'd + r

Dividing this by dd', the first term will not give any remainder as it is a multiple of dd', and the second and third terms are not multiples of dd', giving the remainder to be r'd +r

Therefore, Option A is the correct answer.