27. Find the digit that has the property that if it is appended to the end of any natural number, the resulting number is equal to the sum of three terms, the first of which is the original number, the second is the number represented by the sought digit, and the third is the product of the first two terms.
27. Let the natural number be $a$, and the appended digit be $x$. Then according to the condition $a \cdot 10 + x = a + x + a x$, from which $9 a = a x$, and therefore, $x = 9$.