Factorization of a number to primes

primes.py

# Factorization of a number to primes
from math import sqrt
the_number = 2*3*3*5**3*35*51
primes = []

def factorize(number):
    factor_1 = 1
    factor_2 = 2
    while factor_2 <= int(sqrt(number)):
        if number % factor_2 == 0:
            factor_1 = number // factor_2
            primes.append(factor_2)
            print(f"{number} = {factor_1} * {factor_2}")
            number = factor_1
        else:
            factor_2 += 1
    if len(primes) == 0:
        primes.append(int(the_number)) # the_number is already a prime
    else:
        primes.append(factor_1)

factorize(the_number)
print(primes)