Question

Test the divisibility of each of the following numbers by 11:

(i) 6543207 

(ii) 818532 

(iii) 900163 

(iv) 7531622

Answer 1

(i) 6543207 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 19 and sum of digits in even places = 8 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 6543207 is divisible by 11.

(ii) 818532 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 8 and sum of digits in even places = 19 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 818532 is divisible by 11.

(iii) 900163 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 4 and sum of digits in even places = 15 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 900163 is divisible by 11.

(iv) 7531622 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 18 and sum of digits in even places = 8 

∴ The difference of the sum of alternative digits of a number is 10, which is not divisible by 11. 

Hence, 7531622 is not divisible by 11.