Using divisibility test, 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 = 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.
(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.
(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.
(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.
(e) 10000001 → 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.
(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.

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