Answer :
Sure! To find the prime factorization of 66, we need to express it as a product of its prime numbers. Here's how you can do it step by step:
1. Identify the smallest prime number that divides 66:
- The number 66 is an even number, so it is divisible by 2, which is the smallest prime number.
- Dividing 66 by 2 gives us 33. So, one of the prime factors is 2.
2. Factorize the quotient (33):
- Now we need to factor 33. The smallest prime number that divides 33 is 3.
- Dividing 33 by 3 gives us 11. So, another prime factor is 3.
3. Check if the remaining quotient (11) is a prime number:
- The number 11 is itself a prime number, which means it can only be divided by 1 and 11.
Putting this all together, the prime factorization of 66 is:
[tex]\[ 2 \times 3 \times 11 \][/tex]
Therefore, the correct choice from the options given in the question is H: [tex]\(2 \times 3 \times 11\)[/tex].
1. Identify the smallest prime number that divides 66:
- The number 66 is an even number, so it is divisible by 2, which is the smallest prime number.
- Dividing 66 by 2 gives us 33. So, one of the prime factors is 2.
2. Factorize the quotient (33):
- Now we need to factor 33. The smallest prime number that divides 33 is 3.
- Dividing 33 by 3 gives us 11. So, another prime factor is 3.
3. Check if the remaining quotient (11) is a prime number:
- The number 11 is itself a prime number, which means it can only be divided by 1 and 11.
Putting this all together, the prime factorization of 66 is:
[tex]\[ 2 \times 3 \times 11 \][/tex]
Therefore, the correct choice from the options given in the question is H: [tex]\(2 \times 3 \times 11\)[/tex].
