Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
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]
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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.