How do you find the prime factorisation of 6 digit numbers in your head?
first you check for 3s, then check for 5s, (those are easy checks) then you gotta start checking for all the other primes one by one, from 7 and working your way up. if you rule them all out in order then you only have to go as high as the square root of the number and then you can stop. you can check the primes (like 7 for example) by maniuplating the target number by multiples of 7 until it gets to something recognizably a multiple of 7. there are endless amounts of useful/easy ways to do these manipulations, and you learn more tricks the more you do it