Thank you for visiting Determine the HCF of 330 and 396 using prime factorization The prime factorization is tex HCF 2 1 times 3 1 times 11 1 2. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine the Highest Common Factor (HCF) of 330 and 396 using prime factorization, we follow these steps:
1. Find the prime factors of each number:
- For 330:
- Divide by 2 (smallest prime): [tex]\( 330 \div 2 = 165 \)[/tex]
- 165 is not divisible by 2; check next smallest prime, which is 3: [tex]\( 165 \div 3 = 55 \)[/tex]
- 55 is not divisible by 3; check the next smallest prime, which is 5: [tex]\( 55 \div 5 = 11 \)[/tex]
- 11 is a prime number itself.
- So, the prime factorization of 330 is [tex]\( 2^1 \times 3^1 \times 5^1 \times 11^1 \)[/tex].
- For 396:
- Divide by 2: [tex]\( 396 \div 2 = 198 \)[/tex]
- Divide by 2 again: [tex]\( 198 \div 2 = 99 \)[/tex]
- 99 is not divisible by 2; check next smallest prime, which is 3: [tex]\( 99 \div 3 = 33 \)[/tex]
- Divide by 3 again: [tex]\( 33 \div 3 = 11 \)[/tex]
- 11 is a prime number itself.
- So, the prime factorization of 396 is [tex]\( 2^2 \times 3^2 \times 11^1 \)[/tex].
2. Identify the common prime factors:
- Compare the prime factors of the two numbers.
- Common prime factors are 2, 3, and 11.
3. Take the smallest power of each common factor:
- For 2, the smallest power is [tex]\( 2^1 \)[/tex].
- For 3, the smallest power is [tex]\( 3^1 \)[/tex].
- For 11, the smallest power is [tex]\( 11^1 \)[/tex].
4. Multiply these together to get the HCF:
- [tex]\( HCF = 2^1 \times 3^1 \times 11^1 \)[/tex]
- Calculate the product: [tex]\( 2 \times 3 \times 11 = 66 \)[/tex].
Thus, the HCF of 330 and 396 is 66.
1. Find the prime factors of each number:
- For 330:
- Divide by 2 (smallest prime): [tex]\( 330 \div 2 = 165 \)[/tex]
- 165 is not divisible by 2; check next smallest prime, which is 3: [tex]\( 165 \div 3 = 55 \)[/tex]
- 55 is not divisible by 3; check the next smallest prime, which is 5: [tex]\( 55 \div 5 = 11 \)[/tex]
- 11 is a prime number itself.
- So, the prime factorization of 330 is [tex]\( 2^1 \times 3^1 \times 5^1 \times 11^1 \)[/tex].
- For 396:
- Divide by 2: [tex]\( 396 \div 2 = 198 \)[/tex]
- Divide by 2 again: [tex]\( 198 \div 2 = 99 \)[/tex]
- 99 is not divisible by 2; check next smallest prime, which is 3: [tex]\( 99 \div 3 = 33 \)[/tex]
- Divide by 3 again: [tex]\( 33 \div 3 = 11 \)[/tex]
- 11 is a prime number itself.
- So, the prime factorization of 396 is [tex]\( 2^2 \times 3^2 \times 11^1 \)[/tex].
2. Identify the common prime factors:
- Compare the prime factors of the two numbers.
- Common prime factors are 2, 3, and 11.
3. Take the smallest power of each common factor:
- For 2, the smallest power is [tex]\( 2^1 \)[/tex].
- For 3, the smallest power is [tex]\( 3^1 \)[/tex].
- For 11, the smallest power is [tex]\( 11^1 \)[/tex].
4. Multiply these together to get the HCF:
- [tex]\( HCF = 2^1 \times 3^1 \times 11^1 \)[/tex]
- Calculate the product: [tex]\( 2 \times 3 \times 11 = 66 \)[/tex].
Thus, the HCF of 330 and 396 is 66.
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