how can i swiftly find the factors of large numbers. like say 9450 ?
#9450 factors
opaque ibex
silent yewBOT
neon falcon
how can i swiftly find the factors of large numbers. like say 9450 ?
The answer depends on what type of solution is acceptable for you.
- If you need to get an answer no matter what way just type it in Wolfram alpha and you get the factors.
- If you need to do it for some educational purposes you can write a small program in python or whatever which makes trial divisions of your number N by factors up to sqrt(N).
- If you need to do some really huge factorizations like N>10^100 then you use some special algorithms like NFS and a corresponding software.
- If you need to do exacly this number on paper you see it is ending in 50, so it is divisible by 50. And you are left with 189 which is obviously divisible by 9. And then 21=3*7.
spare robin
how can i swiftly find the factors of large numbers. like say 9450 ?
It's not easy. In fact, the difficulty of factoring large integers is the core of modern cryptography and computer security
opaque ibex
thanks
opaque ibex
It's not easy. In fact, the difficulty of factoring large integers is the core o...
whats so special about them that we use them in cryptography ?
spare robin
whats so special about them that we use them in cryptography ?
A lot of cryptography is based around two principles in number theory:
- Factoring very large numbers is very hard
- Calculating the discrete log is very hard
Cryptography is built around these ideas because, if you already have the solution (e.g. A password), then it is easy to verify that the solution is correct. But if you don't have it, then reverse engineering it is almost impossible.
If I have you some giant 2048 digit number, and I told you what it's factors were, a computer could easily verify whether or not those were the factors. But it would computationally infeasible to find the factors