finding out the way to show $333667$ is a prime number

Question

While doing prime factorization $12345679$

$x=12345679$

$10x=123456790$

$9x=111111111=111×1001001$

$x=37×333667$

we know $37$ is a prime, should I need to find out $333667$ is a prime or not? if yes then how?
(no calculator please)