What is the prime factorization of 24?
Understand the Problem
The question is asking for the prime factorization of the number 24, which involves breaking it down into its prime number factors.
Answer
$2^3 \times 3^1$
Answer for screen readers
The prime factorization of 24 is $2^3 \times 3^1$.
Steps to Solve
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Identify the Number to Factor We start with the number 24 and need to break it down into its prime factors.
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Divide by the Smallest Prime Number The smallest prime number is 2. We divide 24 by 2: $$ 24 \div 2 = 12 $$
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Continue Dividing by 2 Next, we keep dividing by 2 because 12 is even: $$ 12 \div 2 = 6 $$
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Repeat Division by 2 Continue the process with 6: $$ 6 \div 2 = 3 $$
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Divide by the Next Prime Number Now 3 is a prime number itself, so we stop here.
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Combine the Prime Factors The prime factors of 24 are the numbers we divided by: $$ 24 = 2 \times 2 \times 2 \times 3 $$ This can also be written as: $$ 24 = 2^3 \times 3^1 $$
The prime factorization of 24 is $2^3 \times 3^1$.
More Information
The prime factorization expresses a number as a product of prime numbers. Every integer greater than 1 can be expressed uniquely as a product of prime numbers, which is a fundamental principle in number theory. The prime factors of 24 indicate that it is made up of three 2's and one 3.
Tips
- Forgetting to divide by the smallest prime number first.
- Stopping the division process too early before finding all prime factors, especially if a number can be divided further.
