Which of the following numbers is divisible by 45?

Given data

• Test divisibility by 45.

Concept / Approach

• Since 45 = 5 × 9 and gcd(5, 9) = 1, a number is divisible by 45 iff it is divisible by 5 and by 9.
• Divisible by 5 ⇒ last digit is 0 or 5. Divisible by 9 ⇒ sum of digits is a multiple of 9.

Check each option

2700: last digit 0 (✓/5); sum = 2+7+0+0 = 9 (✓/9) ⇒ divisible by 45.1895: last digit 5 (✓/5); sum = 1+8+9+5 = 23 (✗/9) ⇒ not by 45.2235: last digit 5 (✓/5); sum = 2+2+3+5 = 12 (✗/9) ⇒ not by 45.2510: last digit 0 (✓/5); sum = 2+5+1+0 = 8 (✗/9) ⇒ not by 45.

Final Answer

Only 2700 is divisible by 45.