Question:
Find the HCF of 54, 288, and 360.
Find the HCF of 54, 288, and 360.
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To find the HCF, take the lowest power of all common prime factors among the given numbers.
Updated On: Mar 25, 2025
- 18
- 36
- 54
- 108
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The Correct Option is A
Solution and Explanation
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.
- 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.
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