1. The problem is to determine if a given number between 1 and 20 is both prime and divisible by 3. 2. First, recall that a prime number is a number greater than 1 that has no positive divisors other than 1 and itself. 3. Next, check divisibility by 3: a number is divisible by 3 if the remainder when divided by 3 is zero. 4. Since the number must be prime and divisible by 3, we need to find prime numbers between 1 and 20 that are divisible by 3. 5. List prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, 19. 6. Check which of these are divisible by 3: only 3 is divisible by 3. 7. Therefore, the only number between 1 and 20 that is prime and divisible by 3 is 3. 8. The program flowchart would take input $n$ (1 to 20), check if $n$ is prime, then check if $n \bmod 3 = 0$, and print accordingly. Final answer: Only the number 3 satisfies the condition.