To write a program that prompts the user to enter a positive integer and then uses this criterion to determine whether the number is divisible by 11, you can use the following code:```python
# Prompt the user to enter a positive integer
number = int(input("Enter a positive integer: "))
# Determine if the number is divisible by 11
if number % 11 == 0:
print(number, "is divisible by 11")
else:
print(number, "is not divisible by 11")
```In this code, the user is prompted to enter a positive integer using the `input()` function. The `int()` function is used to convert the input string to an integer.The program then determines whether the number is divisible by 11 using the modulus operator `%`. If the remainder of dividing the number by 11 is zero, the number is divisible by 11 and the program prints a message saying so. If the remainder is not zero, the number is not divisible by 11 and the program prints a message saying so.