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Eculid division lemme

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Eculid division lemme

Posted by Savai Singh 5 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 7 months ago

Euclid’s Division Lemma:

A lemma is a proven statement used for proving another statement.

Theorem 1: “Given positive integers a & b, there exist unique integers q & r satisfying a = b*q + r, 0 ≤ r < b”.

E.g. let’s assume that you have 34 apples & you have box that can accommodate 10 apples, then you have put these Apple in 3 boxes & you will have 4 apples remaining. Also note that the remaining apples are less than box size that is 10.

34 Apples = 10 Apples * 3 Box + 4 Apples

If you compare this with Euclid’s Division Lemma

a = b*q + r, 0 ≤ r < b,

Then a = 34, b=10, q=3 & r =4, 0 ≤ 4 <10

1Thank You

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