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Unformatted text preview: ommon divisors of m and r. What does this mean if r = 0. Is the theorem still true? Conclude as a corollary: gcd(m,n) = gcd (m,r). Problem 9
4: Use the result of 9
3 for an algorithm to find the gcd of any two 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. Hint 1: The first step is n = qm + r, with gcd(m,n) = gcd (m,r). The next step is m = q’r + r’. With gcd (m,r) = gcd (r, r’). Notice that the remainder is smaller at each step, so at some point it must...
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 Winter '11
 JamesKing
 Math, Integers

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