Q. 44.3( 23 Votes )

Using divisibility tests, determine which of the following numbers are divisible by 11:

(a) 5445

(b) 10824

(c) 7138965

(d) 70169308

(e) 10000001

(f) 901153

Answer :

Divisibility rule of 11 says that if the difference, of the sum of the digits at odd place and the sum of the digits at even place in the given number, is divisible by 11 then the number is also divisible by 11.


(a) 5445


Calculate the sum of the digits at odd places = 5+4 = 9


Calculate the sum of the digits at even places = 4+5 = 9


Difference = 9-9 = 0


As per the divisibility rule of 11 the difference between the sum of the digits at ood places and the sum of the digits at even places is 0, hence, 5445 is divisible by 11.


(b) 10824


Calculate the sum of the digits at odd places = 4+8+1 = 13


Calculate the sum of the digits at even places = 2+0 = 2


Difference = 13-2 = 11


As per the divisibility rule of 11 the difference between the sum of the digits at ood places and the sum of the digits at even places is 11, which is divisible by 11, therefore 10824 is divisible by 11.


(c) 7138965


Calculate the sum of the digits at odd places = 5+9+3+7 = 24


Calculate the sum of the digits at even places = 6+8+1 = 15


Difference = 24-15 = 9


As the difference between the sum of the digits at ood places and the sum of the digits at even places is 9, which is not divisible by 11, therefore, given number is also not divisible by 11.


(d) 70169308


Calculate the sum of the digits at odd places = 8+3+6+0 = 17


Calculate the sum of the digits at even places = 0+9+1+7 = 17


Difference = 17 – 17 = 0


As per the divisibility rule of 11 the difference between the sum of the digits at ood places and the sum of the digits at even places is 0, hence, 70169308 is divisible by 11.


(e) 10000001


Calculate the sum of the digits at odd places = 1


Calculate the sum of the digits at even places = 1


Difference = 1 – 1 = 0


As per the divisibility rule of 11 the difference between the sum of the digits at ood places and the sum of the digits at even places is 0, hence, 10000001 is divisible by 11.


(f) 901153


Calculate the sum of the digits at odd places = 3+1+0 = 4


Calculate the sum of the digits at even places = 5+1+9 = 15


Difference = 15 – 4 = 11


As per the divisibility rule of 11 the difference between the sum of the digits at ood places and the sum of the digits at even places is 11, which is divible by 11, therefore, 901153 is divisible by 11.


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