from math import sqrt, ceil


# Factorial using for cycle
def factorial_for(n):
    f = 1
    for i in range(1, n+1):
        f = f * i
    return f


# Factorial using while cycle
def factorial_while(n):
    f = 1
    while n > 1:
        f *= n
        n -= 1
    return f

print(factorial_for(6))
print(factorial_while(6))


# Digit sum of number n
def digit_sum(n):
    c = 0
    while n > 0:
        digit = n % 10
        n = n // 10
        c += digit
    return c


# Repeated digit sum of number n
# Applies digit_sum repeatedly on
# number n until one-digit result is found
def repeated_digit_sum(n):
    while n >= 10:
        n = digit_sum(n)
    return n

print(digit_sum(5692))
print(repeated_digit_sum(5692))


# Prints all divisors of a number
def divisors(n):
    for i in range(1, n+1):
        if n % i == 0:
            print(i, end=" ")
    print()
    return 14

divisors(24)  # Just prints the divisors
print(divisors(24))  # Prints the divisors and then the return value 14
a = divisors(24) * 5  # Prints the divisors and stores the return value 14
                      # multiplied by 5 in variable a
print("a =",a)  # Variable a is printed


# Function that returns whether n is a prime number
def is_prime(n):
    # Special value of n=2 treated separately
    if n == 2:
        return True

    # All other cases fall in here
    # The largest number we need to check is sqrt(n)
    for i in range(2, ceil(sqrt(n))+1):
        if n % i == 0:
            # If there is a divisor, we immediately say it is not a prime number
            return False
    # At this point we went through all the numbers that could
    # have divided n, but none of them did. The number is thus a prime.
    return True


print(is_prime(2))


# We can use function is_prime to perform more complex computations


# Prints all the primes less than a limit
def primes_less_than(limit):
    # We go through all the numbers from 2 to the limit
    for j in range(2, limit + 1):
        # If tested number j is prime, we print it
        if is_prime(j):
            print(j, end=" ")
            
            
# Prints k-th prime number
def kth_prime(k):
    # Counter stores how many primes we have already gone through
    counter = 0
    # n is current tested number
    n = 2
    # We cycle as long as we do not have k-th prime number
    while counter < k:
        if is_prime(n):
            # When we have found a prime number, we increase the counter
            counter += 1
        n += 1  # We go through the numbers one by one
    return n - 1  # We return n-1 as even after we found k-th prime number, we increased n

primes_less_than(15)

print(kth_prime(1))
print(kth_prime(100))


# Prints the factorized number
# Note how this function need not use is_prime function
def factorization(n):
    # div is current tested divisor
    div = 2
    # When n == 1 we went through all its divisors
    while n > 1:
        if n % div == 0:
            # When div is n's divisor, we print it and divide n by it
            print(div, end=" ")
            n = n // div
        else:
            # If div does not divide n, we increase it and test another one
            div += 1
    print()
    # return is not here, as we do not want to return any value


factorization(1024)
    

# Converts number from decimal to binary
def convert_10_to_2(x):
    # out stores the binary string
    out = ""
    # We divide x and store the bits until x is 0
    while x > 0:
        bit = str(x % 2)  # bit contains actual remainder after division by 2
                          # This is the bit we obtained
        out = bit + out  # We prepend the output string with found bit
        x = x // 2
    return out


print(convert_10_to_2(42))