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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=728 and b=219461:

a	b	q	r	s1	s2	s3	t1	t2	t3
728	219461	0	728	1	0	1	0	1	0
219461	728	301	333	0	1	-301	1	0	1
728	333	2	62	1	-301	603	0	1	-2
333	62	5	23	-301	603	-3316	1	-2	11
62	23	2	16	603	-3316	7235	-2	11	-24
23	16	1	7	-3316	7235	-10551	11	-24	35
16	7	2	2	7235	-10551	28337	-24	35	-94
7	2	3	1	-10551	28337	-95562	35	-94	317
2	1	2	0	28337	-95562	219461	-94	317	-728

Answer

So we found that:

gcd(728, 219461) = 1
s = -95562
t = 317

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| = |-95562 × 728 + 317 × 219461| = |-69569136 + 69569137| = |1| = 1
gcd(a, b) = gcd(728, 219461) = 1

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