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1. State Euclid's division lemma and apply it to solve the following problems:(i) A number when divided by 27 gives 364 as quotient and 7 as remainderFind the number.(if) Find the number by which 546 should be divided to get 7 as quotient and7 as remainder.

Answer»

Euclid’s division lemma:

Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that a = b × q + r where 0 ≤ r < b.

Euclid’s division lemma can be used to find the highest common factor of any two positive integers and to show the common properties of numbers.

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=>let the number be x

7 should be the quoteient as well as remainder

quoteient is 7 so,

=> 546 = x*7 +7

=>546 = 7x +7

=>7x = 546 - 7

=>7x = 539

=>x = 539/7

=>x = 77

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