State Euclid's division lemma
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Euclid's Division Lemma or Euclid division algorithm states that Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
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If a and b are positive integers such that a=bq+r, then every common divisor of a and b is a common divisor of b and r, and vice-versa
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