Question

Without actual division show that 11 is a factor of each of the following numbers:

(i) 1111
(ii) 11011
(iii) 110011
(iv) 1100011

Answer 1

(i) 1,111

The sum of the digits at the odd places = 1 + 1 = 2

The sum of the digits at the even places = 1 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 1,111 is divisible by 11 because the difference of the sums is zero.

(ii) 11,011

The sum of the digits at the odd places = 1 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 11,011 is divisible by 11 because the difference of the sums is zero.

(iii) 1,10,011

The sum of the digits at the odd places = 1 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 0 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 1,10,011 is divisible by 11 because the difference of the sums is zero.

(iv) 11,00,011

The sum of the digits at the odd places = 1 + 0 + 0 + 1 = 2

The sum of the digits at the even places = 1 + 0 + 1 = 2

The difference of the two sums = 2 − 2 = 0

∴ 11,00,011 is divisible by 11 because the difference of the sums is zero.