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[DOC File]COT 3100 Quiz #9: Euclid's Algorithm 3/23/05
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The Euclidean Algorithm. The Euclidean Algorithm makes repeated use of the division algorithm to find the greatest common divisor of two positive integers. If we are given two positive integers a and b where , then if , then , If , then we compute. The last nonzero remainder, , is the greatest common divisor of a and b, that is, . Note:
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[DOC File]Community College of Philadelphia
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The Euclidean Algorithm is a very useful algorithm for finding the greatest common divisor of any two given integers. Using the Euclidean Algorithm is a tedious task for pairs of large numbers because the algorithm requires a high number of steps to execute.
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[DOC File]Gear Freq. Using Euclidean Algorithm
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One of the consequences of the Euclidean Algorithm is as follows: Given integers a and b, there is always an integral solution to the equation. ax + by = gcd(a,b). Furthermore, the Extended Euclidean Algorithm can be used to find values of x and y to satisfy the equation above. The algorithm will look similar to the proof in some manner.
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Euclidean Algorithm to Calculate Greatest Common Divisor (GCD) o…
The Euclidean Algorithm is a time tested efficient method to find the GCD of two integers, and it can easily be programmed to compute the number of assembly phases for a gear as the following example shows.
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[DOC File]Proof That Euclid’s Algorithm Works
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Thus, gcd(427, 154) = 7. b) Using the Extended Euclidean Algorithm find all pairs of integers x and y that satisfy the equation 427x + 154y = gcd(427, 154). 35 - 2(14) = 7, (6) which is obtained by writing (4) backwards.
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[DOC File]Part one - Florida Atlantic University
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Using Euclidean algorithm calculate GCD (21,300) & GCD (125, 20) [K3 –Apply] (CO1) 4. Find GCD of (1403, 1081) [K3 –Apply] (CO1) 5. Explain Fermat’s little theorem and solve the following [K3 –Apply] (CO1) (i) 15 18 mod 17 (ii) 5 27 mod 13. 6. In a Chinese remainder theorem n=210, n1=5, n2=6 n3=7 and compute j -1 (3, 5, 2) i.e. given ...
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[DOC File]Section 1: Rings and Fields
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113. Use the Euclidean algorithm to find gcd(34 21). Ans: 1. 114. Use the Euclidean Algorithm to find gcd(900 140). Ans: 20. 115. Use the Euclidean Algorithm to find gcd(580 50). Ans: 10. 116. Use the Euclidean Algorithm to find gcd(390 72). Ans: 6. 117. Use the Euclidean Algorithm to find gcd(400 0). Ans: 400. 118. Use the Euclidean Algorithm ...
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[DOC File]Project Report
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The final nonzero remainder is the greatest common divisor of x0 and x1. The Euclidean Algorithm can be summarized like this:; ; ; In this case, is the last nonzero remainder and it is the gcd of x0 and x1. For example, if we need to find gcd (1547, 560) Since 7(21, we are done. The greatest common divisor is the last non-zero remainder: gcd ...
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Find gcd using euclidean algorithm