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
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
(a) 5445
Sum of the digits at odd places = 5 + 4 = 9
Sum of the digits at even places = 4 + 5 = 9
Difference = 9 − 9 = 0
As the difference between the sum of the digits at odd places and the
sum of the digits at even places is 0, therefore, 5445 is divisible
by 11.
(b) 10824
Sum of the digits at odd places = 4 + 8 + 1 = 13
Sum of the digits at even places = 2 + 0 = 2
Difference = 13 − 2 = 11
The difference between the sum of the digits at odd 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
Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
Sum of the digits at even places = 6 + 8 + 1 = 15
Difference = 24 − 15 = 9
The difference between the sum of the digits at odd places and the
sum of digits at even places is 9, which is not divisible by 11.
Therefore, 7138965 is not divisible by 11.
(d) 70169308
Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
Sum of the digits at even places = 0 + 9 + 1 + 7 = 17
Difference = 17 − 17 = 0
As the difference between the sum of the digits at odd places and the
sum of the digits at even places is 0, therefore, 70169308 is
divisible by 11.
(e) 10000001
Sum of the digits at odd places = 1
Sum of the digits at even places = 1
Difference = 1 − 1 = 0
As the difference between the sum of the digits at odd places and the
sum of the digits at even places is 0, therefore, 10000001 is
divisible by 11.
(f) 901153
Sum of the digits at odd places = 3 + 1 + 0 = 4
Sum of the digits at even places = 5 + 1 + 9 = 15
Difference = 15 − 4 = 11
The difference between the sum of the digits at odd places and the
sum of the digits at even places is 11, which is divisible by 11.
Therefore, 901153 is divisible by 11.
(a) 5445
Sum of the digits at odd places = 5 + 4 = 9
Sum of the digits at even places = 4 + 5 = 9
Difference = 9 − 9 = 0
As the difference between the sum of the digits at odd places and the sum of the digits at even places is 0, therefore, 5445 is divisible by 11.
(b) 10824
Sum of the digits at odd places = 4 + 8 + 1 = 13
Sum of the digits at even places = 2 + 0 = 2
Difference = 13 − 2 = 11
The difference between the sum of the digits at odd 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
Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
Sum of the digits at even places = 6 + 8 + 1 = 15
Difference = 24 − 15 = 9
The difference between the sum of the digits at odd places and the sum of digits at even places is 9, which is not divisible by 11. Therefore, 7138965 is not divisible by 11.
(d) 70169308
Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
Sum of the digits at even places = 0 + 9 + 1 + 7 = 17
Difference = 17 − 17 = 0
As the difference between the sum of the digits at odd places and the sum of the digits at even places is 0, therefore, 70169308 is divisible by 11.
(e) 10000001
Sum of the digits at odd places = 1
Sum of the digits at even places = 1
Difference = 1 − 1 = 0
As the difference between the sum of the digits at odd places and the sum of the digits at even places is 0, therefore, 10000001 is divisible by 11.
(f) 901153
Sum of the digits at odd places = 3 + 1 + 0 = 4
Sum of the digits at even places = 5 + 1 + 9 = 15
Difference = 15 − 4 = 11
The difference between the sum of the digits at odd places and the sum of the digits at even places is 11, which is divisible by 11. Therefore, 901153 is divisible by 11.
