EUCLID'S ALGORITHM
\jˈuːklɪdz ˈalɡəɹˌɪθəm], \jˈuːklɪdz ˈalɡəɹˌɪθəm], \j_ˈuː_k_l_ɪ_d_z ˈa_l_ɡ_ə_ɹ_ˌɪ_θ_ə_m]\
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(Or "Euclidean Algorithm") An algorithm forfinding the greatest common divisor (GCD) of two numbers.It relies on the identitygcd(a, b) = gcd(a-b, b)To find the GCD of two numbers by this algorithm, repeatedlyreplace the larger by subtracting the smaller from it untilthe two numbers are equal. E.g. 132, 168 -> 132, 36 -> 96, 36-> 60, 36 -> 24, 36 -> 24, 12 -> 12, 12 so the GCD of 132 and168 is 12.This algorithm requires only subtraction and comparisonoperations but can take a number of steps proportional to thedifference between the initial numbers (e.g. gcd(1, 1001) willtake 1000 steps).
By Denis Howe
Word of the day
Platidiam
- An inorganic water-soluble platinum complex. After undergoing hydrolysis, it reacts DNA produce both intra interstrand crosslinks. These crosslinks appear to impair replication and transcription of DNA. The cytotoxicity cisplatin correlates with cellular arrest in G2 phase cell cycle.