Euclid's algorithm
时间: 2024-01-29 17:02:58 浏览: 23
Euclid's algorithm is a method for finding the greatest common divisor (GCD) of two integers. The algorithm is based on the observation that if a and b are two integers with a > b, then the GCD of a and b is the same as the GCD of b and the remainder of a divided by b.
The algorithm can be expressed as follows:
1. Let a and b be the two integers for which we want to find the GCD.
2. If b is 0, then the GCD of a and b is a.
3. Otherwise, compute the remainder r of a divided by b.
4. Set a to be equal to b, and set b to be equal to r.
5. Repeat steps 2-4 until b is 0.
6. The GCD of a and b is the final value of a.
For example, let's find the GCD of 60 and 48 using Euclid's algorithm:
1. Let a = 60 and b = 48.
2. Compute the remainder r of 60 divided by 48, which is 12.
3. Set a to be equal to b (a = 48) and set b to be equal to r (b = 12).
4. Compute the remainder r of 48 divided by 12, which is 0.
5. Since b is 0, the GCD of 60 and 48 is the final value of a, which is 12.
Therefore, the GCD of 60 and 48 is 12.
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