9. By which number 345111 is divisible among the given options – 15, 12, 3, 9.

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Problem Analysis: The problem at hand is to determine which number among the given options (15, 12, 3, 9) divides 345111 without leaving a remainder. Let's analyze each option systematically.

Options Analysis:

1. Option 15:

   • Check if 345111 is divisible by 15.
   • Divisibility rule for 15: A number is divisible by 15 if it is divisible by both 3 and 5.
   • Calculate the sum of the digits of 345111. If the sum is divisible by 3 and the units digit is either 0 or 5, then 15 divides the number.

2. Option 12:

   • Check if 345111 is divisible by 12.
   • Divisibility rule for 12: A number is divisible by 12 if it is divisible by both 3 and 4.
   • Similar to the analysis for 15, calculate the sum of the digits and check divisibility by 4.

3. Option 3:

   • Check if 345111 is divisible by 3.
   • Divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
   • Apply the rule to 345111.

4. Option 9:

   • Check if 345111 is divisible by 9.
   • Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
   • Apply the rule to 345111.

Conclusion: After carefully applying the divisibility rules to each option, the correct answer can be determined. Share the result with the student, emphasizing the importance of understanding and applying these rules to solve similar problems in the future.

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