Solution Exercise 760: a python algorithm to finds the list of all prim divisors for given integer.

Exercise 760

Write an algorithm in python as a function that finds the list of all prime divisors of a given integer n.

Solution

# creating a function to test primality of given number
def testPrimality(n):
    # initializing the number of divisors of n
    numberDivisors = 0
    for i in range(1 , n + 1):
        # we test if i is a divisor of n
        if n%i == 0:
            # and then we increment the number of divisors
            numberDivisors = numberDivisors + 1 
        # the number n is prim if and only if admits exactly two divisors 1 and itself 
    if numberDivisors == 2:
        return True
    else:
        return False

# creating a function that returns the list of prim divisors of n 
def listPrimDivisors(n):
    # initializing the list of prim divisors
    primDivisors = []
    for i in range(1 , n + 1):
        if( n%i == 0 and testPrimality(i)):
            primDivisors.append(i)
    return primDivisors

# Testing algorithm
print("List of all prim divisors of 42 is : listPrimDivisors(42) = " , listPrimDivisors(42))
# The output is : List of all prim divisors of 42 is : listPrimDivisors(42) =  [2, 3, 7]