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# num02 - Number Theory Computing the GCD One way of...

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Number Theory Computing the GCD One way of computing the GCD of two integers is listing all of their divisors and picking out the largest one common to each. pause But this is highly inefficient for large numbers. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 10

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Number Theory Computing the GCD One way of computing the GCD of two integers is listing all of their divisors and picking out the largest one common to each. pause But this is highly inefficient for large numbers. A more efficient process involves repeated use of the Division Algorithm, and first appeared in Euclid’s book Elements . MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 10
Number Theory Computing the GCD One way of computing the GCD of two integers is listing all of their divisors and picking out the largest one common to each. pause But this is highly inefficient for large numbers. A more efficient process involves repeated use of the Division Algorithm, and first appeared in Euclid’s book Elements . Consequently, this process is called the Euclidean Algorithm and it is fast. . . MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 10

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Number Theory Computing the GCD One way of computing the GCD of two integers is listing all of their divisors and picking out the largest one common to each. pause But this is highly inefficient for large numbers. A more efficient process involves repeated use of the Division Algorithm, and first appeared in Euclid’s book Elements . Consequently, this process is called the Euclidean Algorithm and it is fast. . . very fast! MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 10
Number Theory The Euclidean Algorithm We are trying to compute gcd ( a ; b ) . Watch how we Apply the Division algorithm repeatedly until we get a remainder of 0.

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