Question

Find the HCF of 54, 288, and 360.

• A. 18
• B. 36
• C. 54
• D. 108

Hint:

To find the HCF, take the lowest power of all common prime factors among the given numbers.

Answer 1

The Correct Option is A

We find the prime factorization of each number:
- 54 = \( 2^1 \times 3^3 \)
- 288 = \( 2^5 \times 3^2 \)
- 360 = \( 2^3 \times 3^2 \times 5^1 \)
Now, taking the **minimum power** of each common factor:
\[ HCF = 2^1 \times 3^2 \] \[ = 2 \times 9 = 18 \]
Thus, the HCF is 18.