I have an assignment to factor a 160 digit number on the form p*q, where p and q are primes. The number is N in RSA. I also got e, which is also about 160 digits, and the fact that d is much much smaller than e. I assume the latter information was given because we need to use it to factor N in reasonable time, but I can't figure out how to do this.

All I know is that e*d = 1 mod (p-1)(q-1). Can't seem to find a way to calculate neither d nor p or q, since there's too many unknown in the equation.

Any help would be very appreciated.