Question

Show that following numbers are divisible 11 and 12 by using

divisibility rules.

a) 6259 b) 2364

c) 813505 d) 92436​

Answer 1

A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11.

(i) 5918

Sum of digits at odd places = 5 + 1 = 6 and,

Sum of digits at even places = 9 + 8 = 17

Their difference = 17 - 6 = 11

Since difference is 11 which is divisible by 11, therefore 5918 is divisible by 11.

(ii) 68,717

Sum of digits at odd places = 6 + 7 + 7 = 20

And sum of digits at even places = 8 + 1 = 9

Difference = 20 - 9 = 11

Since difference is 11 which is divisible by 11, therefore 68,717 is divisible by 11

(iii) 3882

Sum of digits at odd places = 3 + 8 = 11 and,

Sum of digits at even places = 8 + 2 = 10

Difference = 11 - 10 = 1

Since difference is 1 which is not divisible by 11, therefore 3882 is not divisible by 11.

(iv) 10857

Sum of digits at odd places = 1 + 8 + 7 = 16

And, sum of digits at even places = 0 + 5 = 5