Question

Given positive integers a and b such that a > bthere exist unique integers q and rsatisfying a = bq + r , 0 ≤ r < b. "

This statement is called Euclid's Division Lemma.

Given a = 3654 and b = 144 find q and rsatisfying the above conditions.
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Answer 1

Given :   positive integers a and b such that a > b there exist unique integers q and r satisfying a = bq + r , 0 ≤ r < b. "

To find : q and r when a = 3654 and b = 144

Solution:

a = bq  + r

0 ≤ r < b

                    25

    144    _|   3654   |_

                    288

                  _____

                     774      

                     720

                    _____

                       54

3654 = 144 * 25   +   54

q  = 25

r =  54

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