Question

When 200 is divided by a positive integer x, the remainder is 8. How many values of x are there?​

Answer 1

Given :

200 is divided by a positive integer x.

The remainder is :

=8

To Find :

Values of x = ?

Solution :

∴200 is divisible by x , so according to Euclidean Algorithm :

200 = qx + r ;

where q is quotient and r is remainder obtained on dividing 200 by x.

So , 200 = xq + 8  -(1)

∴The remainder is always less than the divisior , so :

x > 8  .

Now from eq 1 we have ;

xq = 200 -8

xq = 192

Now from the prime factorisation of 192 :

$192 = 2\times 2\times 2\times 2\times 2\times 2\times 3$

So , we see that 192 is divisible by 2, 3, 4 , 6 , 8 , 12 , 14 , 16 , 24 , 32, 64 and 192

But we want x > 8

So the values of x are 12 , 14 , 16 , 24 . 32 , 64 and 192.