Write a note on Euclid's division lemma
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EUCLID'S DIVISION LEMMA
If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.
For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019, and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well.
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Definition: Euclid's Division Lemma states that, if two positive integers “a” and “b”, then there exists unique integers “q” and “r” such that which satisfies the condition a = bq + r where 0 ≤ r ≤ b.
Step-by-step explanation:
In this example, 9 is the divisor, 58 is the dividend, 6 is the quotient and 4 is the remainder.
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