Thank you for visiting Determine the HCF Highest Common Factor of 330 and 396 using prime factorization. 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 HCF (Highest Common Factor) of 330 and 396 using prime factorization, we can follow these steps:
1. Prime Factorization of 330:
- Start with the smallest prime number, 2. Since 330 is even, it's divisible by 2:
[tex]\[ 330 ÷ 2 = 165 \][/tex]
- Now, try the next smallest prime number, 3. Since the sum of the digits of 165 is 12, which is divisible by 3, 165 is divisible by 3:
[tex]\[ 165 ÷ 3 = 55 \][/tex]
- Move to the next prime number, 5. Since 55 ends with a 5, it is divisible by 5:
[tex]\[ 55 ÷ 5 = 11 \][/tex]
- Finally, 11 is a prime number.
- Therefore, the prime factors of 330 are: [tex]\[ 2, 3, 5, 11 \][/tex]
2. Prime Factorization of 396:
- Start with 2 again, since 396 is even:
[tex]\[ 396 ÷ 2 = 198 \][/tex]
- Divide by 2 again, since 198 is also even:
[tex]\[ 198 ÷ 2 = 99 \][/tex]
- Try 3, since the sum of the digits of 99 is 18, divisible by 3:
[tex]\[ 99 ÷ 3 = 33 \][/tex]
- Divide by 3 once more, as 33 is also divisible by 3:
[tex]\[ 33 ÷ 3 = 11 \][/tex]
- Finally, 11 is a prime number.
- Therefore, the prime factors of 396 are: [tex]\[ 2, 2, 3, 3, 11 \][/tex]
3. Identify the Common Prime Factors:
- The common prime factors between 330 and 396 are: [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
4. Calculate the HCF:
- For each common factor, take the smallest power that appears in the factorization of both numbers.
- 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].
- Multiply these smallest powers together to get the HCF:
[tex]\[ HCF = 2^1 \times 3^1 \times 11^1 = 2 \times 3 \times 11 = 66 \][/tex]
Therefore, the HCF of 330 and 396 is 66.
1. Prime Factorization of 330:
- Start with the smallest prime number, 2. Since 330 is even, it's divisible by 2:
[tex]\[ 330 ÷ 2 = 165 \][/tex]
- Now, try the next smallest prime number, 3. Since the sum of the digits of 165 is 12, which is divisible by 3, 165 is divisible by 3:
[tex]\[ 165 ÷ 3 = 55 \][/tex]
- Move to the next prime number, 5. Since 55 ends with a 5, it is divisible by 5:
[tex]\[ 55 ÷ 5 = 11 \][/tex]
- Finally, 11 is a prime number.
- Therefore, the prime factors of 330 are: [tex]\[ 2, 3, 5, 11 \][/tex]
2. Prime Factorization of 396:
- Start with 2 again, since 396 is even:
[tex]\[ 396 ÷ 2 = 198 \][/tex]
- Divide by 2 again, since 198 is also even:
[tex]\[ 198 ÷ 2 = 99 \][/tex]
- Try 3, since the sum of the digits of 99 is 18, divisible by 3:
[tex]\[ 99 ÷ 3 = 33 \][/tex]
- Divide by 3 once more, as 33 is also divisible by 3:
[tex]\[ 33 ÷ 3 = 11 \][/tex]
- Finally, 11 is a prime number.
- Therefore, the prime factors of 396 are: [tex]\[ 2, 2, 3, 3, 11 \][/tex]
3. Identify the Common Prime Factors:
- The common prime factors between 330 and 396 are: [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
4. Calculate the HCF:
- For each common factor, take the smallest power that appears in the factorization of both numbers.
- 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].
- Multiply these smallest powers together to get the HCF:
[tex]\[ HCF = 2^1 \times 3^1 \times 11^1 = 2 \times 3 \times 11 = 66 \][/tex]
Therefore, the HCF of 330 and 396 is 66.
Thank you for reading the article Determine the HCF Highest Common Factor of 330 and 396 using prime factorization. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
