How to find the factors of large numbers fast

You make the number smaller by dividing by prime numbers first 2, 3, 5, 7 and 11. 

Mostly it will reduce the number unless its a prime number or a multiple of a prime number greater than 11

506 divided by 2 gives 253. 

253 cannot be divided by 3,5 or 7. How do I know its not divisible so quickly? I use the divisibility test.

A number is divisible by 2 if the last number is even. 
A number is divisible by 3 if the sum of the digits is divisible by 3
A number is divisible by 5 if the last digits are 0 or 5. 
For 7 you need to actually divide to check. 
So we try 11. 

253 divided by 11 gives 23
23 is also a prime number so we can’t reduce it further. 

This is the only way to reduce it.
 
You can combine the prime factors together if you want to reduce steps. 
For example, the prime numbers of 506 is 2, 11 and 23. 
We can combine 2 and 11 to get 22.
So we are left with 22 x 23. 

Hope this helps