Question

Let pqr be a three digit number. Then, pqr + qrp + rpq is always divisible by which numbers?

Answer 1

pqr = 100p + 10q + r

qrp = 100 q + 10r + p

rpq = 100r + 10p + q

Adding all three,
$\Rightarrow$ pqr + qrp + rpq = 100(p + q +r) + 10(p + q + r) + (p + q + r) = 111 (p + q +r) = 37 $\times$ 3 (p + q + r)

(pqr + qrp + rpq) is always divisible by 1, 3, 37, 111 and (p + q + r).