Determine the hcf of 330 and 396 using prime factorization

General
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determine the hcf of 330 and 396 using prime factorization

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To determine the highest common factor (HCF) of 330 and 396 using prime factorization, we need to find the prime factors of both numbers and identify the common factors.

Let’s start by finding the prime factors of 330:

  1. Divide 330 by the smallest prime number, which is 2. The result is 165.
  2. Divide 165 by 3. The result is 55.
  3. Divide 55 by 5. The result is 11.

So, the prime factors of 330 are 2 x 3 x 5 x 11.

Now, let’s find the prime factors of 396:

  1. Divide 396 by 2. The result is 198.
  2. Divide 198 by 2. The result is 99.
  3. Divide 99 by 3. The result is 33.
  4. Divide 33 by 3. The result is 11.

So, the prime factors of 396 are 2 x 2 x 3 x 3 x 11.

To find the HCF, we need to identify the common prime factors and multiply them together. In this case, the common prime factor is 11.

Therefore, the HCF of 330 and 396 is 11.