# Probability 1/8100 to guess it successfully

**Number Theory**Level 3

I am given 2 four-digit positive integers \(A = \overline{xyzw} \) and \(B = \overline{wzyx} \) such that:

If \(A\) is divided by the sum of its digits, it gives a quotient of 327 and remainder of 14.

If \(B\) is divided by the sum of its digits, it gives a quotient of 227 and remainder of 16.

Find the value of the integer \(A\).