Question

Find q, r in \mathbb{Z} so that 105 = 11q + r

with 0 \leq r < 11 as in the division algorithm

Answer 1

`q=9\,,\,r=6`

Explanation:

Division Algorithm :

As per division algorithm , for numbers a and b , there exist numbers q and r such that
`a=bq+r\,\,,0\leq r< b`

Here ,

a = Dividend

b = Divisor

q = quotient

r = remainder

Given : 105 = 11q + r such that
`0 \leq r < 11`

Here, clearly a = 105 , b = 11

To find : q and r

Solution : On dividing 105 by 11 , we get
`105=11* 9+6`

On comparing
`105=11* 9+6` with
`a=bq+r\,\,,0\leq r< b` , we get
`q=9\,,\,r=6`