discrete mathematics - Prove that a number with 30 digits cannot have more than 100 prime factors.

I know that the a number with more than 100 prime factors must be larger than

$2 ^ {100}$, so it must have more than 30 digits but i am having trouble with proof.

I was given
Hint: every prime number is $≥ 2$.

Can someone help me connect the two ideas.