factorize + eratho_sieve

def factorize(num):
    n = num
    upper = num
    primes = eratho(upper)
    result = []
    while num > 1:
        for i in range(len(primes)):
            if num % primes[i] == 0:
                result.append(primes[i])
                num = num // primes[i]
    result.sort()
    print(n, "=", end=" ")
    for i in range(len(result)):
        if i<len(result)-1:
            print(result[i], "* ", end="")
        else:
            print(result[i])


def eratho(n):
    result = []
    printer = []
    for i in range(n+1):
        result.append(True)
    for j in range(n+1):
        if j <= 1:
            result[j] = False
        else:
            for i in range(2, n+1):
                if j % i == 0 and j != i:
                    result[j] = False
    for i in range(len(result)):
        if result[i]:
            printer.append(i)
    return(printer)