13.100. Determine the positive integer based on the following data: if it is written in digits and the digit 4 is appended to the right, the resulting number is divisible without a remainder by a number that is 4 greater than the sought number, and the quotient is a number that is 27 less than the divisor.
Solution.

Let $x$ be the required number. According to the condition $\frac{10 x+4}{x+4}=x+4-27$, from which $x=32$.

Answer: 32.