Mathematics
Examine the following numbers for divisibility by 11:
(i) 10428
(ii) 70169803
(iii) 7136985
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Answer
A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or divisible by 11.
(i) 10428
Sum of digits at odd places (from right) = 8 + 4 + 1 = 13
Sum of digits at even places (from right) = 2 + 0 = 2
Difference = 13 − 2 = 11, which is divisible by 11.
Hence, 10428 is divisible by 11.
(ii) 70169803
Sum of digits at odd places (from right) = 3 + 8 + 6 + 0 = 17
Sum of digits at even places (from right) = 0 + 9 + 1 + 7 = 17
Difference = 17 − 17 = 0.
Hence, 70169803 is divisible by 11.
(iii) 7136985
Sum of digits at odd places (from right) = 5 + 9 + 3 + 7 = 24
Sum of digits at even places (from right) = 8 + 6 + 1 = 15
Difference = 24 − 15 = 9, which is not divisible by 11.
Hence, 7136985 is not divisible by 11.
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