To determine the correct prime factorization of [tex]\( 24 \)[/tex], let's follow a systematic approach step by step:
1. Start with the smallest prime number: 2.
Since [tex]\( 24 \)[/tex] is an even number, it is divisible by [tex]\( 2 \)[/tex].
[tex]\( 24 \div 2 = 12 \)[/tex]
So, one factor of [tex]\( 24 \)[/tex] is [tex]\( 2 \)[/tex].
2. Continue factoring the quotient: 12.
[tex]\( 12 \)[/tex] is also an even number, so it is again divisible by [tex]\( 2 \)[/tex].
[tex]\( 12 \div 2 = 6 \)[/tex]
Now we have another factor of [tex]\( 2 \)[/tex].
3. Continue factoring the quotient: 6.
[tex]\( 6 \)[/tex] is still an even number, so it is divisible again by [tex]\( 2 \)[/tex].
[tex]\( 6 \div 2 = 3 \)[/tex]
Now we have a third factor of [tex]\( 2 \)[/tex].
4. Now we are left with 3.
[tex]\( 3 \)[/tex] is a prime number and cannot be factored further unless we use [tex]\( 1 \)[/tex].
Now we have completely factored [tex]\( 24 \)[/tex] down to its prime factors. The prime factors we found are three [tex]\( 2 \)[/tex]'s and one [tex]\( 3 \)[/tex].
So, the factorization of [tex]\( 24 \)[/tex] is:
[tex]\[ 24 = 2 \cdot 2 \cdot 2 \cdot 3 \][/tex]
Thus, the correct prime factorization of [tex]\( 24 \)[/tex] corresponds to the given option:
[tex]\[ 2 \cdot 2 \cdot 2 \cdot 3 \][/tex]
So, the correct choice is:
[tex]\[ 2 \cdot 2 \cdot 2 \cdot 3 \][/tex]
