Finding large prime factors (number theory)

[bremenfallturm]

Homework Statement

Find the prime factorizations of 314000.

Relevant Equations

Unsure - I've tried a couple of different methods as explained in the post

Hello!

I'm asked to factor 314000 by hand. The answer key says that is is $2^4\cdot 5^3\cdot 157$, but I honestly have no idea how to factor it by hand.

I know that I can check all prime numbers up to $\sqrt{314000}$ but that would not be doable by hand obviously.
I did try to use the method that this video suggests:
(Which basically is: try to divide by 2, try to divide by 3, try to divide by 5, try to divide by 7)
But the problem is that $157$ is a factor.
How can I factor the number by hand?

 

[fresh_42]

Where is the problem?
$$
314000=314\cdot 1000=2\cdot 157 \cdot (10^3)=2\cdot 157\cdot (2\cdot 5)^3=2^4\cdot5^3\cdot 157
$$

 

[bremenfallturm]

Oh you're right. Sometimes you're just intimidated by a problem I guess. The problem is nowhere now.