To determine which of the numbers is divisible by 11, we can apply the divisibility rule for 11. The rule states:

• To check if a number is divisible by 11, find the difference between the sum of its digits in odd positions and the sum of its digits in even positions. If the result is divisible by 11 (or equals 0), then the number is divisible by 11.

Let's check each number:

1. 253614

   • Odd positions: 2, 3, 1 → $2 + 3 + 1 = 6$
   • Even positions: 5, 6, 4 → $5 + 6 + 4 = 15$
   • Difference: $6 - 15 = -9$
   • $-9$ is not divisible by 11, so 253614 is not divisible by 11.

2. 4126547

   • Odd positions: 4, 2, 5, 7 → $4 + 2 + 5 + 7 = 18$
   • Even positions: 1, 6, 4 → $1 + 6 + 4 = 11$
   • Difference: $18 - 11 = 7$
   • 7 is not divisible by 11, so 4126547 is not divisible by 11.

3. 542146

   • Odd positions: 5, 2, 4 → $5 + 2 + 4 = 11$
   • Even positions: 4, 1, 6 → $4 + 1 + 6 = 11$
   • Difference: $11 - 11 = 0$
   • Since the difference is 0, 542146 is divisible by 11.

4. 9076185

   • Odd positions: 9, 7, 1, 5 → $9 + 7 + 1 + 5 = 22$
   • Even positions: 0, 6, 8 → $0 + 6 + 8 = 14$
   • Difference: $22 - 14 = 8$
   • 8 is not divisible by 11, so 9076185 is not divisible by 11.

Conclusion:

The number 542146 is divisible by 11.

Would you like more details, or have any further questions?

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Here are 5 related questions:

1. How do you determine divisibility by 7?
2. What is the general method for checking divisibility by 13?
3. Can divisibility rules be applied to fractions?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. How can you check if a number is divisible by 3?

Tip: When checking divisibility by large numbers, factor them into primes for easier checks.