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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=961 and b=380385:

a	b	q	r	s1	s2	s3	t1	t2	t3
961	380385	0	961	1	0	1	0	1	0
380385	961	395	790	0	1	-395	1	0	1
961	790	1	171	1	-395	396	0	1	-1
790	171	4	106	-395	396	-1979	1	-1	5
171	106	1	65	396	-1979	2375	-1	5	-6
106	65	1	41	-1979	2375	-4354	5	-6	11
65	41	1	24	2375	-4354	6729	-6	11	-17
41	24	1	17	-4354	6729	-11083	11	-17	28
24	17	1	7	6729	-11083	17812	-17	28	-45
17	7	2	3	-11083	17812	-46707	28	-45	118
7	3	2	1	17812	-46707	111226	-45	118	-281
3	1	3	0	-46707	111226	-380385	118	-281	961

Answer

So we found that:

gcd(961, 380385) = 1
s = 111226
t = -281

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| = |111226 × 961 + -281 × 380385| = |106888186 + -106888185| = |1| = 1
gcd(a, b) = gcd(961, 380385) = 1

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