how long will it take to factorise a 100-digit number?

Answer 1

Well, I just tested it with a random 100 digit number - it took my computer 8 minutes 45 seconds to factor the number 51051 39834 52137 87733 31794 63341 78075 02211 89976 25203 73089 81736 30001 54139 71499 61020 74568 78846 11957 37948 into 2² * 3 * 56 00143 * 5791 44395 57622 11692 97621 * 6 40820 71791 64943 63704 40249 03441 * 204 69341 76437 37217 86692 04656 17148 72023. Thus I assume that in the average case a 100 digit number will take about 10 minutes. It could take shorter or longer, however, depending on the factors in your particular number. Here's the factoring applet I used:
http://alpertron.com.ar/ECM.htm

Answer 2

by hand or with a computer?

It could take forever or more by hand!

A few examples would be easier like 1e100 = 10^99 = 5^99*2^99.
Some would be impossible ie 100 digit primes! But it would take a long time to check them by hand!

two 50 digit primes multiplied together would be really tough.

Since about n/log(n) is the number of primes to check, you would only have to check 10^47 numbers. If your PC can do 1 per nanosecond, it could be done in 10^24 years!

Of course there are tricks to improve your chances!

Answer 3

Depends on the number. Factorizing one googol for example would be easy (2^100*5^100). Factorizing a googol plus one, not so easy.

Answer 4

it depands on how complex the number is... if it is multiple of simple factors (2,3,5,7,11) then it might take between 2-5 minutes... otherwise, between 15-20 minutes

Answer 5

It depends.
If you use a computer program, of course that would reduce how much time it would take.

Answer 6

It depends, if its prime then no time at all!