Find the number which is completely divisible by 45.

Step-by-Step Solution

To determine if a number is divisible by 45, we must check for divisibility by its coprime factors, which are 5 and 9 (since 5 * 9 = 45).

1. Divisibility Rule for 5: A number is divisible by 5 if it ends in 0 or 5.

2. Divisibility Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Analyzing the Options

• Option A: 306990

  • Ends in 0 (Divisible by 5).

  • Sum of digits = 3 + 0 + 6 + 9 + 9 + 0 = 27.

  • 27 is divisible by 9.

  • Result: Divisible by 45.

• Option B: 331145

  • Ends in 5 (Divisible by 5).

  • Sum of digits = 3 + 3 + 1 + 1 + 4 + 5 = 17.

  • 17 is not divisible by 9.

  • Result: Not divisible by 45.

• Option C: 256987

  • Does not end in 0 or 5.

  • Result: Not divisible by 45.

• Option D: 181660

  • Ends in 0 (Divisible by 5).

  • Sum of digits = 1 + 8 + 1 + 6 + 6 + 0 = 22.

  • 22 is not divisible by 9.

  • Result: Not divisible by 45.