13. The greatest of the common divisors of two non-zero natural numbers is called the greatest common divisor (GCD) of these two numbers. If the GCD of two non-zero natural numbers is 1, then these two numbers are called coprime or relatively prime. For example, 2 and 3 are coprime, 3 and 8 are coprime; 12 and 15 are not coprime, because their GCD is 3. Among the natural numbers not exceeding 81, there are  numbers that are coprime with 81.
Analysis:
$81=3^{4}, 81$ has only the prime factor 3, so all numbers containing the factor 3 are not coprime with 81, $81 \div 3=27$, there are 27 numbers not greater than 81 that contain the factor 3, the remaining numbers are coprime with 81, $81-27=54$ numbers.