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StudyMath# The greatest common divisor of two integers

##### This calculator determines the greatest common divisor of two integers using Euclidean algorithm

The greatest common divisor of two integers m and n is the largest integer that divides them both.

This calculator determines the greatest common divisor of two integers using Euclidean algorithm

Euclidean algorithm is very simple.

You start building sequnce of numbers. First one is greatest of two integers, second is opposite, third is remainder of division of two previous numbers, forth is remainder of division of second and third one, etc. Last remainder before zero is the answer.

I'll show by example.

Suppose we need to find GCD for 13 and 17

1 step. Create initial sequence

**17, 13**

2 step. Third member is the remainder of division of 17 to 13

**17, 13, 4**

3 step. Forth member is the remainder of division of 13 to 4

**17, 13, 4, 1**

4 step. Fifth member is the remainder of division of 4 to 1

**17, 13, 4, 1, 0**

1 is the last remainder before 0, so, this is our answer.

And numbers those GCD is 1 are called **prime numbers**

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