Divisible by 91!!

Note that $91\times11=1001$ . If we multiply this by $111$ we obtain $111111$ , thus the answer is $6$ .

start with 111 and start doing long division by 91. if you get a remainder add another 1 to the dividend (111). keep doing this till the remainder becomes 0. you will see when 111111 comes the remainder is zero. therefore x = 6 => it will be divisible by 6 (question should mention that we have to select the largest number but anyhow)

This method will only work if the number of 1's are less as it will get tedious if not

Every time 6 ones are together ...it is divisible by 91...so x is divisible by 6