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Using the Euclid's algorithm find the multiplicative inverse of 1234 mod4321?
Using the extended Euclidean algorithm, find the multiplicative inverse of a) 1234 mod 4321
What is Euclid's ladder?
The greatest common factor (GCF), also known as the greatest common divisor (GCD), represents the largest number that divides into each member of a set of numbers. Smaller GCFs can be quickly calculated using the prime factors of each number, but calculating large GCFs the same way is sometimes difficult. An algorithm devised by Euclid, (the ladder) lets you find the GCF of any number without extensive factoring. All you need is the ability to do long division.
What is Euclid's Algorithm?
Euclid's algorithm is a popular algorithm to compute the GCD of two numbers. Algorithm: Gcd(a,b) = Gcd(b, a mod b), where a>=b and Gcd(a,0) = a Say we want to find the GCD of 72 and 105. 105 mod 72 = 33, so GCD(72,105) = GCD(33,72) 72 mod 33 = 6, so GCD(33,72) = GCD(6,33) 33 mod 6 = 3 so GCD(6,33) = GCD(3,6) 6 mod 3 = 0 so GCD(3,6) = GCD(0,3) = 3. So the GCD of 72 and 105 is 3.
Find the greatest common divisor in of 11 plus 7i and 18-i?
Use the division algorithm. If b = pa + r, then gcd(b,a) = gcd(a,r). Then you can apply the division algorithm again with a = qr + r' and gcd(a,r) = gcd(r, r'). Note that each time the square norm of the remainder gets smaller and smaller, so eventually this process will terminate and you can get the answer. Here, it should be 1.
Was there any contribution of euclid in the discovery of pi or something related to circles?
While Euclid was famed for his development and presentation of geometry to the ancient Greek world, it was Archimedes who made a direct contribution to the discovery of pi.I suggest you find an online summary of Euclid's Elementsand use that as a resource.
