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Answer :
To find the Highest Common Factor (HCF) of 330 and 396 using prime factorization, follow these steps:
1. Prime Factorize 330:
- Start by dividing by the smallest prime number, 2.
- 330 ÷ 2 = 165
- Next, use the next smallest prime number, 3.
- 165 ÷ 3 = 55
- Now, try 5.
- 55 ÷ 5 = 11
- Finally, 11 is a prime number.
Therefore, the prime factorization of 330 is:
[tex]\(2 \times 3 \times 5 \times 11\)[/tex]
2. Prime Factorize 396:
- Begin with 2, since 396 is even.
- 396 ÷ 2 = 198
- 198 ÷ 2 = 99
- Next, divide by 3.
- 99 ÷ 3 = 33
- Divide by 3 again.
- 33 ÷ 3 = 11
- 11 is a prime number.
Therefore, the prime factorization of 396 is:
[tex]\(2 \times 2 \times 3 \times 3 \times 11\)[/tex]
3. Identify Common Factors:
- From the prime factorizations, identify the prime numbers present in both.
- The common prime factors are: 2, 3, and 11.
4. Calculate the HCF:
- Multiply the lowest power of all common factors together.
- [tex]\(HCF = 2^1 \times 3^1 \times 11^1 = 66\)[/tex]
So, the HCF of 330 and 396 is 66.
1. Prime Factorize 330:
- Start by dividing by the smallest prime number, 2.
- 330 ÷ 2 = 165
- Next, use the next smallest prime number, 3.
- 165 ÷ 3 = 55
- Now, try 5.
- 55 ÷ 5 = 11
- Finally, 11 is a prime number.
Therefore, the prime factorization of 330 is:
[tex]\(2 \times 3 \times 5 \times 11\)[/tex]
2. Prime Factorize 396:
- Begin with 2, since 396 is even.
- 396 ÷ 2 = 198
- 198 ÷ 2 = 99
- Next, divide by 3.
- 99 ÷ 3 = 33
- Divide by 3 again.
- 33 ÷ 3 = 11
- 11 is a prime number.
Therefore, the prime factorization of 396 is:
[tex]\(2 \times 2 \times 3 \times 3 \times 11\)[/tex]
3. Identify Common Factors:
- From the prime factorizations, identify the prime numbers present in both.
- The common prime factors are: 2, 3, and 11.
4. Calculate the HCF:
- Multiply the lowest power of all common factors together.
- [tex]\(HCF = 2^1 \times 3^1 \times 11^1 = 66\)[/tex]
So, the HCF of 330 and 396 is 66.
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