Question

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

1. 5445
2. 10824
3. 7138965
4. 70169308
5. 10000001
6. 901153

Answer 1

(a) 5445
\(→\) Sum of the digits at odd places = 4 + 5 = 9
\(→\) Sum of the digits at even places = 4 + 5 = 9
\(→\) Difference of both sums = 9 – 9 = 0
Since the difference is 0, therefore, the number is divisible by 11.

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(b) 10824
\(→\) Sum of the digits at odd places = 4 + 8 +1 = 13
\(→\) Sum of the digits at even places = 2 + 0 = 2
\(→\) Difference of both sums = 13 – 2 = 11
Since the difference is 11, therefore, the number is divisible by 11.

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(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 of both sums = 24 – 15 = 9
Since the difference is neither 0 nor 11, therefore, the number is not divisible by 11.

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(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 of both sums = 17 – 17 = 0
Since the difference is 0, therefore, the number is divisible by 11.

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\(→\) Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1
\(→\) Sum of the digits at even places = 0 + 0 + 0 + 1 = 1
\(→\) Difference of both sums = 1 – 1 = 0
Since the difference is 0, therefore, the number is divisible by 11. 

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(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 of both sums = 15 – 4 = 11
Since the difference is 11, therefore, the number is divisible by 11.