Euclids Division Lemma

Euclid's division lemma states that " For any two positive integers a and b, there exist integers q and r such that a=bq+r , 0≤r<b.

If we divide a/b,then we get q as the quotient and r as the remainder such that it satisfies a=bq+r  where

                           r,remainder is greater than or equal to zero

                           b,divisor is always greater than the remainder r

                           

When the divisor b is perfectly divisible then remainder r is zero,if not divisible remainder is less than divisor  

a-dividend                                                                           

b - divisor

q - quotient

r-remainder

Dividend =divisor*quotient + remainder

consider the examples

 

 22/7 

Dividing 22/7 gives 3 as quotient and 1 as remainder                                      

22-dividend                                                                           

7 - divisor

3- quotient

1-remainder

Here 7 is greater than 1,so we can write 22/7 as 

22=7*3 + 1  ,0≤ 1< 7

81/9

81=9*9, here remainder is zero ,ie 0<9

58/5

58=5*11+ 3 , 0≤ 3< 5

In all the above cases r is greater than or equal to zero and less than b.