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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:

Euclidean Algorithm
For the basics and the table notation
Extended Euclidean Algorithm
Unless you only want to use this calculator for the basic Euclidean Algorithm.
Modular multiplicative inverse
in case you are interested in calculating the modular multiplicative inverse of a number modulo n
using the Extended Euclidean Algorithm

Input

Algorithm

Choose which algorithm you would like to use.

Numbers

Enter the input numbers:

Output

This is the output of the Extended Euclidean Algorithm using the numbers a=503 and b=195943:

a	b	q	r	s1	s2	s3	t1	t2	t3
503	195943	0	503	1	0	1	0	1	0
195943	503	389	276	0	1	-389	1	0	1
503	276	1	227	1	-389	390	0	1	-1
276	227	1	49	-389	390	-779	1	-1	2
227	49	4	31	390	-779	3506	-1	2	-9
49	31	1	18	-779	3506	-4285	2	-9	11
31	18	1	13	3506	-4285	7791	-9	11	-20
18	13	1	5	-4285	7791	-12076	11	-20	31
13	5	2	3	7791	-12076	31943	-20	31	-82
5	3	1	2	-12076	31943	-44019	31	-82	113
3	2	1	1	31943	-44019	75962	-82	113	-195
2	1	2	0	-44019	75962	-195943	113	-195	503

Answer

So we found that:

gcd(503, 195943) = 1
s = 75962
t = -195

Verification
If our answer is correct, then the absolute value of s × a + t × b is equal to the gcd of a and b. We have:

|s × a + t × b| = |75962 × 503 + -195 × 195943| = |38208886 + -38208885| = |1| = 1
gcd(a, b) = gcd(503, 195943) = 1

As you can see, |s × a + t × b| = gcd(a, b), so our calculation is correct!