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Calculator

For the Euclidean Algorithm, Extended Euclidean Algorithm and multiplicative inverse.

Before you use this calculator

If you're used to a different notation, the output of the calculator might confuse you at first.
Even though this is basically the same as the notation you expect. If that happens, don't panic.
Just make sure to have a look the following pages first and then it will all make sense:


Input

Algorithm

Choose which algorithm you would like to use.

Numbers

Enter the input numbers. Note that you need to enter n before b.
E.g. if you want to know the multiplicative inverse of 26 mod 11, then use n=11 and b=26.

n=
b=


Output

This is the calculation for finding the multiplicative inverse of 21208 mod 235 using the Extended Euclidean Algorithm:
nbqr t1t2t3
235212080235010
212082359058101
235584301-4
5831911-477
3130-477-235
Answer

So t = 77. Now we still have to apply mod n to that number:
77 mod 235 ≡ 77
So the multiplicative inverse of 21208 modulo 235 is 77.

Verification

Let i be the answer we just found, so i=77. We also have b=21208 and n=235.
If our answer is correct, then i × b (mod n) ≡ 1 (mod n).
Let's see if that's indeed the case.
i × b (mod n) ≡
77 × 21208 (mod 235) ≡
1633016 (mod 235) ≡
1 (mod 235)