Euclid's Algorithm in English

(With some Algebra thrown in)

 

 

Step

Task

1

Assign the value of the larger number to M, and the smaller number to N

2

Divide M by N (M/N) and assign the remainder to R

3

If R is not 0, then assign M the value of N, assign N the value of R, and return to step 2

If R = 0, then the GCD is N and the algorithm terminates

Notice that in Step 3 there are two different possibilities. This is typically how algorithms work. There usually needs to be some terminating condition, otherwise the algorithm (program) runs forever.

 

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