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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 15433 mod 412 using the Extended Euclidean Algorithm:
nbqr t1t2t3
412154330412010
1543341237189101
41218923401-2
189345191-211
3419115-211-13
19151411-1324
15433-1324-85
431124-85109
3130-85109-412
Answer

So t = 109. Now we still have to apply mod n to that number:
109 mod 412 ≡ 109
So the multiplicative inverse of 15433 modulo 412 is 109.

Verification

Let i be the answer we just found, so i=109. We also have b=15433 and n=412.
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) ≡
109 × 15433 (mod 412) ≡
1682197 (mod 412) ≡
1 (mod 412)