And now the max of r1 r2 is less than m 2 so at each

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Unformatted text preview: o integers that does not require factoring them into prime factors. Then use your algorithm on some non ­obvious numbers, including some of at least 4 digits and preferably more. Answer: This is called the Euclidean Algorithm. First of all, for divisors are the same for positive or negative integers, so we assume that m and n are positive. If we wish to find a common divisor of m and n, we use the division algorithm to write n = qm + r, with 0 ≤ r < m as before. Because of 9 ­3, the gcd of m and n is the same as the gcd of m and r. If r = 0 above, then m divides n the gcd = m. But we note that now, whatever, n was, the maximum of m and r is m. Then if we apply the division algorithm to m , we get m = q1r+ r1, with r1 < r. So now the divisors of m and n are the same as the divisors of m and r which are the same as the devisors of r and r1. And we n...
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This note was uploaded on 01/29/2014 for the course MATH 300A taught by Professor Jamesking during the Winter '11 term at University of Washington.

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