We need to find the count of positive integers less than 20 that are co-prime to 20.

Use Euler's totient formula $\phi(n) = n \times \frac{p_1-1}{p_1} \times \frac{p_2-1}{p_2}$ where $p_1, p_2$ are distinct prime factors of $n$. For $20 = 2^2 \times 5$, calculate $20 \times (1 - 1/2) \times (1 - 1/5) = 20 \times 1/2 \times 4/5 = 8$.

Many students mistake co-prime integers for prime numbers, or they include 1 and 20 in the set, but 20 is not less than 20 and 20 is not co-prime to 20.

This concept is fundamental in modular arithmetic and RSA cryptography, where calculating the totient of a product of two large primes is a security requirement.