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6. Determine the HCF of 330 and 396 using prime factorization.
To find the Highest Common Factor (HCF), we need to perform the prime factorization of both numbers:
1. Prime factorization of 330:
- 330 is even, so divide by 2: [tex]\( 330 \div 2 = 165 \)[/tex]
- 165 is divisible by 3: [tex]\( 165 \div 3 = 55 \)[/tex]
- 55 is divisible by 5: [tex]\( 55 \div 5 = 11 \)[/tex]
- 11 is a prime number.
So, the prime factors of 330 are [tex]\( 2, 3, 5, \)[/tex] and [tex]\( 11 \)[/tex].
[tex]\( 330 = 2^1 \times 3^1 \times 5^1 \times 11^1 \)[/tex].
2. Prime factorization of 396:
- 396 is even, so divide by 2: [tex]\( 396 \div 2 = 198 \)[/tex]
- 198 is even, so divide by 2 again: [tex]\( 198 \div 2 = 99 \)[/tex]
- 99 is divisible by 3: [tex]\( 99 \div 3 = 33 \)[/tex]
- 33 is divisible by 3: [tex]\( 33 \div 3 = 11 \)[/tex]
- 11 is a prime number.
So, the prime factors of 396 are [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
[tex]\( 396 = 2^2 \times 3^2 \times 11^1 \)[/tex].
3. Find the HCF:
- Identify common prime factors: [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
- For each common prime, use the lowest power:
- For 2: lowest power is [tex]\( 2^1 \)[/tex].
- For 3: lowest power is [tex]\( 3^1 \)[/tex].
- For 11: lowest power is [tex]\( 11^1 \)[/tex].
Multiply these together: [tex]\( 2^1 \times 3^1 \times 11^1 = 66 \)[/tex].
Therefore, the HCF of 330 and 396 is 66.
7. Calculate [tex]\( 4319675 + 5299999 \)[/tex]
Add the two numbers directly:
- [tex]\( 4319675 + 5299999 = 9619674 \)[/tex]
Therefore, the sum of [tex]\( 4319675 \)[/tex] and [tex]\( 5299999 \)[/tex] is 9619674.
6. Determine the HCF of 330 and 396 using prime factorization.
To find the Highest Common Factor (HCF), we need to perform the prime factorization of both numbers:
1. Prime factorization of 330:
- 330 is even, so divide by 2: [tex]\( 330 \div 2 = 165 \)[/tex]
- 165 is divisible by 3: [tex]\( 165 \div 3 = 55 \)[/tex]
- 55 is divisible by 5: [tex]\( 55 \div 5 = 11 \)[/tex]
- 11 is a prime number.
So, the prime factors of 330 are [tex]\( 2, 3, 5, \)[/tex] and [tex]\( 11 \)[/tex].
[tex]\( 330 = 2^1 \times 3^1 \times 5^1 \times 11^1 \)[/tex].
2. Prime factorization of 396:
- 396 is even, so divide by 2: [tex]\( 396 \div 2 = 198 \)[/tex]
- 198 is even, so divide by 2 again: [tex]\( 198 \div 2 = 99 \)[/tex]
- 99 is divisible by 3: [tex]\( 99 \div 3 = 33 \)[/tex]
- 33 is divisible by 3: [tex]\( 33 \div 3 = 11 \)[/tex]
- 11 is a prime number.
So, the prime factors of 396 are [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
[tex]\( 396 = 2^2 \times 3^2 \times 11^1 \)[/tex].
3. Find the HCF:
- Identify common prime factors: [tex]\( 2, 3, \)[/tex] and [tex]\( 11 \)[/tex].
- For each common prime, use the lowest power:
- For 2: lowest power is [tex]\( 2^1 \)[/tex].
- For 3: lowest power is [tex]\( 3^1 \)[/tex].
- For 11: lowest power is [tex]\( 11^1 \)[/tex].
Multiply these together: [tex]\( 2^1 \times 3^1 \times 11^1 = 66 \)[/tex].
Therefore, the HCF of 330 and 396 is 66.
7. Calculate [tex]\( 4319675 + 5299999 \)[/tex]
Add the two numbers directly:
- [tex]\( 4319675 + 5299999 = 9619674 \)[/tex]
Therefore, the sum of [tex]\( 4319675 \)[/tex] and [tex]\( 5299999 \)[/tex] is 9619674.
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