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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=881 and b=10379:

a	b	q	r	s1	s2	s3	t1	t2	t3
881	10379	0	881	1	0	1	0	1	0
10379	881	11	688	0	1	-11	1	0	1
881	688	1	193	1	-11	12	0	1	-1
688	193	3	109	-11	12	-47	1	-1	4
193	109	1	84	12	-47	59	-1	4	-5
109	84	1	25	-47	59	-106	4	-5	9
84	25	3	9	59	-106	377	-5	9	-32
25	9	2	7	-106	377	-860	9	-32	73
9	7	1	2	377	-860	1237	-32	73	-105
7	2	3	1	-860	1237	-4571	73	-105	388
2	1	2	0	1237	-4571	10379	-105	388	-881

Answer

So we found that:

$gcd(881, 10379) = 1$
$s = -4571$
$t = 388$

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| = |-4571 × 881 + 388 × 10379| = |-4027051 + 4027052| = |1| = $ $1$
$gcd(a, b) = gcd(881, 10379) = $ $1$

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