Which among the given options is completely divisible by 45?

To determine if a number is divisible by 45, we must check if it is divisible by the coprime factors of 45, which are 5 and 9.

Divisibility Rules

• Divisibility by 5: The last digit must be 0 or 5.

• Divisibility by 9: The sum of all the digits must be divisible by 9.

Step-by-Step Analysis of Options

• Option A: 202860

  • Rule for 5: Ends in 0, so it is divisible by 5.

  • Rule for 9: Sum of digits = 2 + 0 + 2 + 8 + 6 + 0 = 18. Since 18 is divisible by 9, it is divisible by 9.

  • Conclusion: Divisible by both 5 and 9, so it is divisible by 45.

• Option B: 234567

  • Rule for 5: Ends in 7, so it is not divisible by 5.

• Option C: 3456778

  • Rule for 5: Ends in 8, so it is not divisible by 5.

• Option D: 998765

  • Rule for 5: Ends in 5, so it is divisible by 5.

  • Rule for 9: Sum of digits = 9 + 9 + 8 + 7 + 6 + 5 = 44. Since 44 is not divisible by 9, it is not divisible by 9.

Summary

• Option A is the only number that satisfies both conditions (ends in 0 and has a digit sum divisible by 9).