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Answer :
Final answer:
The Highest Common Factor (HCF) of 330 and 396 is 66. This is found by conducting a prime factorization of both numbers, identifying the common factors, and multiplying the lowest power of these common primes.
Explanation:
To find the Highest Common Factor (HCF) of two numbers using prime factorization, we first have to break down each number into its prime factors.
- The prime factorization of 330 is: 2 x 3 x 5 x 11.
- The prime factorization of 396 is: 2 x 2 x 3 x 3 x 11.
Next, we compare the prime factors of both numbers. The common factors are 2, 3, and 11. However, the HCF is found by multiplying the lowest power of the common prime factors.
So, the HCF = 2 x 3 x 11 = 66.
Hence, none of the provided options is correct. Always remember: the Highest Common Factor (HCF) is found by multiplying the lowest powers of the common prime factors obtained through prime factorization.
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The HCF of 330 and 396 is found using prime factorization, which gives us the result of 66.
The Highest Common Factor (HCF) of two numbers using prime factorization is found by expressing each number as a product of its prime factors and then taking the product of the smallest powers of common primes.
For the numbers 330 and 396, let's find their prime factors:
330 = 2 * 3 * 5 * 11
396 = 2 * 2 * 3 * 3 * 11
The common prime factors are 2, 3, and 11. Since 2 appears only once in the prime factorization of 330, and 3 appears once as well (it appears more times in 396, but we take the lowest power), we take these for the HCF: 2 * 3 * 11 = 66.
Therefore, the HCF of 330 and 396 is not among the provided options. The correct answer is 66.
