Write the prime factorization of 24.

Understand the Problem

The question is asking for the prime factorization of the number 24. This means we need to express 24 as a product of its prime numbers.

Answer

The prime factorization of 24 is $2^3 \times 3^1$.
Answer for screen readers

The prime factorization of 24 is $2^3 \times 3^1$.

Steps to Solve

  1. Identify the smallest prime number
    Start with the smallest prime number, which is 2. Check if 2 can divide 24 without leaving a remainder.

  2. Divide by the smallest prime
    Since $24 \div 2 = 12$, we can say that 24 can be expressed as $2 \times 12$. Now, we need to factor 12.

  3. Continue factoring
    Next, take 12. Again, divide it by 2:
    $$12 \div 2 = 6$$
    So now we have $24 = 2 \times 2 \times 6$.

  4. Factor the next number
    Now take 6 and divide by 2 again:
    $$6 \div 2 = 3$$
    So we continue to factor:
    $$24 = 2 \times 2 \times 2 \times 3$$

  5. Express as prime factors
    Now we can write 24 as a product of prime factors:
    $$24 = 2^3 \times 3^1$$

  6. Write the final answer
    Ensure to present the complete factorization clearly.

The prime factorization of 24 is $2^3 \times 3^1$.

More Information

Prime factorization is a way of expressing a number as the product of its prime factors. Recognizing the prime numbers helps in various areas of mathematics, including number theory and arithmetic.

Tips

  • Confusing composite numbers with prime numbers: Always ensure you are dividing by prime numbers.
  • Forgetting to continue factoring down to prime numbers: Keep dividing until all factors are prime.
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