Answer :

Let's solve the two parts of the question step-by-step.

### Part 1: Simplifying the Expression

We need to simplify the expression:
[tex]\[ 10 + 12 - (8 - 3) \][/tex]

Let's break it down:

1. Inside the parentheses, calculate [tex]\(8 - 3\)[/tex]:
[tex]\[ 8 - 3 = 5 \][/tex]

2. Substitute the result back into the expression:
[tex]\[ 10 + 12 - 5 \][/tex]

3. Add and subtract from left to right:
[tex]\[ 10 + 12 = 22 \][/tex]
[tex]\[ 22 - 5 = 17 \][/tex]

So, the simplified result is 17.

### Part 2: Determining the HCF of 330 and 396 Using Prime Factorization

To find the Highest Common Factor (HCF) using prime factorization, follow these steps:

1. Prime Factorization of 330:
- Divide 330 by the smallest prime number 2: [tex]\(330 \div 2 = 165\)[/tex]
- Divide 165 by the smallest prime number 3: [tex]\(165 \div 3 = 55\)[/tex]
- Divide 55 by the smallest prime number 5: [tex]\(55 \div 5 = 11\)[/tex]
- Finally, 11 is a prime number.

So, the prime factors of 330 are [tex]\(2, 3, 5, \text{and } 11\)[/tex].

2. Prime Factorization of 396:
- Divide 396 by the smallest prime number 2: [tex]\(396 \div 2 = 198\)[/tex]
- Divide 198 by 2: [tex]\(198 \div 2 = 99\)[/tex]
- Divide 99 by the smallest prime number 3: [tex]\(99 \div 3 = 33\)[/tex]
- Divide 33 by 3: [tex]\(33 \div 3 = 11\)[/tex]
- Finally, 11 is a prime number.

So, the prime factors of 396 are [tex]\(2, 3, \text{and } 11\)[/tex].

3. Identify Common Prime Factors:
- The common prime factors of 330 and 396 are [tex]\(2, 3, \text{and } 11\)[/tex].

4. Calculate the HCF:
- Multiply the common prime factors:
[tex]\[ HCF = 2 \times 3 \times 11 = 66 \][/tex]

Thus, the HCF of 330 and 396 is 66.

Thank you for reading the article Determine the highest common factor HCF 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!

Rewritten by : Jeany

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