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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

Solution:

We will be using the concepts of divisibility by 11 to solve this.

A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11.

(a) Given number = 5445
Sum of the digits at odd places = 5 + 4 = 9 and sum of the digits at even places = 4 + 5 = 9
Difference = 9 – 9 = 0, which is divisible by 11.
Therefore, the number 5445 is divisible by 11.

(b) Given number = 10824
Sum of the digits at odd places = 4 + 8 + 1 = 13 and Sum of the digits at even places = 2 + 0 = 2
Difference = 13 – 2 = 11, which is divisible by 11.
Therefore, the number 10824 is divisible by 11.

(c) Given number = 7138965
Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24 and Sum of the digits at even places = 6 + 8 + 1 = 15
Difference = 24 – 15 = 9, which is not divisible by 11.
Therefore, the number 7138965 is not divisible by 11.

(d) Given number = 70169308
Sum of digits at odd places = 0 + 9 + 1 + 7 = 17 and Sum of all the digits at even places = 8 + 3 + 6 + 0 = 17
Difference = 17-17 = 0, which is divisible by 11.
Therefore, the number 70169308 is divisible by 11.

(e) Given number = 10000001
Sum of all the digits at odd places = 1 + 0 + 0 + 0 = 1 and Sum of the digits at even places = 0 + 0 + 0 + 1 = 1
Difference = 1 – 1 = 0, which is divisible by 11.
Therefore, the number 10000001 is divisible by 11.

(f) Given number = 901153
Sum of all the digits at odd places = 9 + 1 + 5 = 15 and Sum of the digits at even places = 0 + 1 + 3 = 4
Difference = 15 - 4 = 11, which is divisible by 11.
Therefore, the number 901153 is divisible by 11.

You can also use the Online Divisibility Calculator to check this.

NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 Question 4

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

Summary:

The numbers divisible by 11 are (a) 5445 (b) 10824 (d) 70169308 (e) 10000001, and (f) 901153

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