Answer :
To find the prime factorization of 66, we'll need to break it down into its prime factors step-by-step. Here’s how you can do it:
1. Start with the smallest prime number, which is 2. Check if 66 is divisible by 2:
- 66 divided by 2 equals 33. So, 2 is one of the prime factors.
2. Now, take the quotient, which is 33, and continue factoring:
- Check the next smallest prime number, which is 3. Is 33 divisible by 3?
- 33 divided by 3 equals 11. So, 3 is another prime factor.
3. Finally, check if the last quotient, which is 11, is a prime number:
- 11 is a prime number. Thus, it is one of the prime factors.
Putting all these factors together, the prime factors of 66 are 2, 3, and 11. So, the prime factorization of 66 is:
[tex]\[ 2 \times 3 \times 11 \][/tex]
The correct answer is option H: [tex]\(2 \times 3 \times 11\)[/tex].
1. Start with the smallest prime number, which is 2. Check if 66 is divisible by 2:
- 66 divided by 2 equals 33. So, 2 is one of the prime factors.
2. Now, take the quotient, which is 33, and continue factoring:
- Check the next smallest prime number, which is 3. Is 33 divisible by 3?
- 33 divided by 3 equals 11. So, 3 is another prime factor.
3. Finally, check if the last quotient, which is 11, is a prime number:
- 11 is a prime number. Thus, it is one of the prime factors.
Putting all these factors together, the prime factors of 66 are 2, 3, and 11. So, the prime factorization of 66 is:
[tex]\[ 2 \times 3 \times 11 \][/tex]
The correct answer is option H: [tex]\(2 \times 3 \times 11\)[/tex].
