def smallest_factor(n):
    """prec: n is an integer, n >= 1.
    if n == 1, return 1
    return the smallest factor of n that is >=2.
    """
    if n%2 == 0:
        return 2
    i = 3
    while i *i <= n:
        if n%i == 0:
            return i
        i += 2
    return n
    
def prime_factorization(n):
    """ prec: n >= 1. If n == 1, return []
    otherwise, return a list containing the prime factors of n"""
    if n == 1:
        return []
    d = smallest_factor(n)
    return [d] + prime_factorization(n//d)

x = 111
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 1
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 8
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 215
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 997
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 1000000007
print(f"smallest_factor({x}) = {smallest_factor(x)}")
x = 111
print(f"prime_factorization({x}) = {prime_factorization(x)}")
x = 1
print(f"prime_factorization({x}) = {prime_factorization(x)}")
x = 8
print(f"prime_factorization({x}) = {prime_factorization(x)}")
x = 215
print(f"prime_factorization({x}) = {prime_factorization(x)}")
x = 997
print(f"prime_factorization({x}) = {prime_factorization(x)}")
x = 1000000007
print(f"prime_factorization({x}) = {prime_factorization(x)}")