Factorizing N to derive D So I have the value of N. I have to use this value of N to find the value of D.
N = 265291078722948385089717069136983657793
Now I read about RSA algos and found out that
N=PQ | where P and Q are prime factors 

I found -
P - 14716976826788780483
Q - 18026193955816294571


The following is an example of what I've approached
Choose p = 3 and q = 11
Compute n = p * q = 3 * 11 = 33
Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
Choose e such that 1 &lt; e &lt; φ(n) and e and n are coprime. Let e = 7
Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3 [(3 * 7) % 20 = 1]

We have
P = 14716976826788780483
Q = 18026193955816294571
N = 265291078722948385089717069136983657793
E = 65537 (given)
φ(n) = 265291078722948385056973898354378582740    [using (p-1)(q-1)]


I'm unable to solve the equation  (d * e) % φ(n) = 1 for the above values.
We need to find/derive D.
I tried using this online calculator
Princeton Extended Calc
But it doesn't accept large values
Any help is appreciated
Wolfram alpha can do this:

http://www.wolframalpha.com/input/?i=multiplicative+inverse+of+65537+mod+265291078722948385056973898354378582740

yields 

d = 240894030773496778838526583320400223673

The alternative is to write a small C program using gmp or using python, e.g.