You are looking for the modular inverse of e (mod n), which can be computed using the extended Euclidean algorithm:
function inverse(x, m)
a, b, u := 0, m, 1
while x > 0
q := b // x # integer division
x, a, b, u := b % x, u, x, a - q * u
if b == 1 return a % m
error "must be coprime"
Thus, in your examples, inverse(17, 3120)
= 2753 and inverse(2621, 8736)
= 4373. If you don't want to implement the algorithm, you can ask Wolfram|Alpha for the answer.