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Greatest common divisor

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2. (a) Determine gcd(987, 320).

(b) Determine integers x and y such that 987x + 320y = gcd(987, 320).

3. (a) Determine gcd(−2193, 1008).

(b) Determine integers x and y such that 1008x − 2193y = gcd(−2193, 1008).

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The solution provides examples of working with greatest common divisors. Functions are solved.

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since 987 = 7*47 and 320 = 2^6 * 5 have no prime factors in common, they are relatively prime, i.e. their gcd = 1.

also, 987 = 3 (320) + 27

320 = 11 (27) + 23

27 = 1(23) + 4

23 = 5(4) + 3

4 = 1(3) + 1

3 = 3(1) + 0

so the gcd is indeed 1

to find x, y, ...

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