Check whether the given numbers are divisible by 11 or not?

(a) 786764

(b) 536393

(c) 110011

(d) 1210121

(e) 758043

(f) 8338472

(g) 54678

(h) 13431

(i) 423423

(j) 168861

To determine whether a number is divisible by 11, we can use a specific rule based on the digits of the number. The rule states that a number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11. Let's apply this rule to each of the numbers you've provided.

Step-by-Step Analysis

We'll break down each number, calculate the sums of the digits in odd and even positions, and then check the divisibility condition.

1. Analyzing 786764

• Odd positions: 7 (1st), 6 (3rd), 6 (5th) → Sum = 7 + 6 + 6 = 19
• Even positions: 8 (2nd), 7 (4th), 4 (6th) → Sum = 8 + 7 + 4 = 19
• Difference: |19 - 19| = 0 (divisible by 11)

Result: 786764 is divisible by 11.

2. Analyzing 536393

• Odd positions: 5 (1st), 6 (3rd), 9 (5th) → Sum = 5 + 6 + 9 = 20
• Even positions: 3 (2nd), 3 (4th), 3 (6th) → Sum = 3 + 3 + 3 = 9
• Difference: |20 - 9| = 11 (divisible by 11)

Result: 536393 is divisible by 11.

3. Analyzing 110011

• Odd positions: 1 (1st), 0 (3rd), 1 (5th) → Sum = 1 + 0 + 1 = 2
• Even positions: 1 (2nd), 0 (4th), 1 (6th) → Sum = 1 + 0 + 1 = 2
• Difference: |2 - 2| = 0 (divisible by 11)

Result: 110011 is divisible by 11.

4. Analyzing 1210121

• Odd positions: 1 (1st), 1 (3rd), 1 (5th), 1 (7th) → Sum = 1 + 1 + 1 + 1 = 4
• Even positions: 2 (2nd), 0 (4th), 2 (6th) → Sum = 2 + 0 + 2 = 4
• Difference: |4 - 4| = 0 (divisible by 11)

Result: 1210121 is divisible by 11.

5. Analyzing 758043

• Odd positions: 7 (1st), 8 (3rd), 4 (5th) → Sum = 7 + 8 + 4 = 19
• Even positions: 5 (2nd), 0 (4th), 3 (6th) → Sum = 5 + 0 + 3 = 8
• Difference: |19 - 8| = 11 (divisible by 11)

Result: 758043 is divisible by 11.

6. Analyzing 8338472

• Odd positions: 8 (1st), 3 (3rd), 4 (5th), 2 (7th) → Sum = 8 + 3 + 4 + 2 = 17
• Even positions: 3 (2nd), 8 (4th), 7 (6th) → Sum = 3 + 8 + 7 = 18
• Difference: |17 - 18| = 1 (not divisible by 11)

Result: 8338472 is not divisible by 11.

7. Analyzing 54678

• Odd positions: 5 (1st), 6 (3rd), 8 (5th) → Sum = 5 + 6 + 8 = 19
• Even positions: 4 (2nd), 7 (4th) → Sum = 4 + 7 = 11
• Difference: |19 - 11| = 8 (not divisible by 11)

Result: 54678 is not divisible by 11.

8. Analyzing 13431

• Odd positions: 1 (1st), 4 (3rd), 1 (5th) → Sum = 1 + 4 + 1 = 6
• Even positions: 3 (2nd), 3 (4th) → Sum = 3 + 3 = 6
• Difference: |6 - 6| = 0 (divisible by 11)

Result: 13431 is divisible by 11.

9. Analyzing 423423

• Odd positions: 4 (1st), 3 (3rd), 2 (5th) → Sum = 4 + 3 + 2 = 9
• Even positions: 2 (2nd), 4 (4th), 3 (6th) → Sum = 2 + 4 + 3 = 9
• Difference: |9 - 9| = 0 (divisible by 11)

Result: 423423 is divisible by 11.

10. Analyzing 168861

• Odd positions: 1 (1st), 8 (3rd), 6 (5th) → Sum =