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24 as a product of prime factors

Understand the Problem

The question is asking us to express the number 24 as a product of its prime factors. This involves breaking down 24 into prime numbers that multiply together to give 24.

Answer

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

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

Steps to Solve

  1. Start with the number 24

Begin by dividing 24 by the smallest prime number, which is 2.

$$ 24 \div 2 = 12 $$

  1. Continue factoring 12

Next, we take the result, which is 12, and divide it by 2 again.

$$ 12 \div 2 = 6 $$

  1. Factor 6

Now we factor the next result, which is 6, by dividing it by 2 once more.

$$ 6 \div 2 = 3 $$

  1. Final prime factor

At this point, we have 3, which is a prime number. So we can stop here.

  1. Write down all prime factors

Now we list the prime factors we used:

  • 2 (appears three times)
  • 3 (appears one time)

Thus, the prime factorization of 24 is:

$$ 24 = 2^3 \times 3^1 $$

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

More Information

Prime factorization helps to understand the building blocks of a number. It can be useful in various areas of mathematics, such as simplifying fractions or finding the greatest common divisor.

Tips

Common mistakes include:

  • Stopping too early and not fully decomposing the number, missing that 3 is also a factor.
  • Forgetting to count the number of occurrences of the prime factors (e.g., not recognizing that 2 appears three times).
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