08소인수분해

def prime_factors(n):

    factors = []

    divisor = 2

    while n > 1:

        while n % divisor == 0:

            factors.append(divisor)

            n //= divisor

        divisor += 1

    return factors if len(factors) > 0 else [n]

def factorization_string(factors):

    factor_count = {}

    for factor in factors:

        if factor in factor_count:

            factor_count[factor] += 1

        else:

            factor_count[factor] = 1

    factors_str = ' * '.join([f"{k}" + (f'^{v}' if v > 1 else '') for k, v in factor_count.items()])

    return factors_str

# 사용자로부터 수 입력 받기

user_input = int(input("정수를 입력하세요: "))

if user_input <= 1:

    print("1 이상의 정수를 입력해주세요.")

else:

    result = prime_factors(user_input)

    factorization = factorization_string(result)

    print(f"{user_input}의 소인수분해 결과: {factorization}")