Short Answer 
To find the HCF (Highest Common Factor) of 330 and 396, first determine their prime factorizations: 330 = 2 * 3 * 5 * 11 and 396 = 2^2 * 3^2 * 11. The common prime factors are 2, 3, and 11, and taking the lowest powers yields the HCF as 66, calculated by multiplying these factors (2 * 3 * 11).
Step 1: Find the Prime Factors
Start by expressing each number in terms of its prime factors. For the numbers 330 and 396, the prime factorizations are:
- 330 = 2 * 3 * 5 * 11
- 396 = 2 * 2 * 3 * 3 * 11
This breakdown allows you to see which prime numbers make up each number.
Step 2: Identify Common Prime Factors
Next, identify the common prime factors between the two sets of prime factors derived in the first step. The common primes for 330 and 396 are:
- 2
- 3
- 11
Make sure to consider the lowest powers in which these primes appear in both factorizations to find the HCF.
Step 3: Calculate the HCF
Finally, multiply the common prime factors together, taking the smallest power of each. As seen in the previous step:
- From 2, we take 21
- From 3, we take 31
- From 11, we take 111
The calculation yields 2 * 3 * 11 = 66. Thus, the HCF of 330 and 396 is 66.