
    Design a function for an adaptive learning platform that calculates the total number of shared difficulty levels between two student assessment scores, where these shared levels represent suitable intermediate learning steps for student progression. The function should take two assessment scores as input and return the sum of all their common factors, which will be used to determine balanced learning paths that are appropriately challenging for the student.
    

    
def sum(a, b):
    """
    Design a function for an adaptive learning platform that calculates the total number of shared difficulty levels between two student assessment scores, where these shared levels represent suitable intermediate learning steps for student progression. The function should take two assessment scores as input and return the sum of all their common factors, which will be used to determine balanced learning paths that are appropriately challenging for the student.
    

    """
def sum(a, b):
    """
    Design a function for an adaptive learning platform that calculates the total number of shared difficulty levels between two student assessment scores, where these shared levels represent suitable intermediate learning steps for student progression. The function should take two assessment scores as input and return the sum of all their common factors, which will be used to determine balanced learning paths that are appropriately challenging for the student.
    

    """
    sum = 0
    for i in range(1, min(a, b)):
        if a % i == 0 and b % i == 0:
            sum += i
    return sum