What is the largest number that will divide both 81 and 54 perfectly, with no remainder?

• A. 9
• B. 18
• C. 54
• D. 27

Answer: (D)

The largest number that will divide both 81 and 54 evenly is their greatest common divisor. To find it, factor each number: 81 = 3^4 and 54 = 2 × 3^3. The shared factor is 3^3, which is 27. So 27 divides both numbers (81 ÷ 27 = 3 and 54 ÷ 27 = 2). Any larger divisor would require a factor not present in one of the numbers, such as a 2, which doesn’t divide 81. Therefore, the greatest common divisor is 27.