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
- Start with the number 24
Begin by dividing 24 by the smallest prime number, which is 2.
$$ 24 \div 2 = 12 $$
- Continue factoring 12
Next, we take the result, which is 12, and divide it by 2 again.
$$ 12 \div 2 = 6 $$
- Factor 6
Now we factor the next result, which is 6, by dividing it by 2 once more.
$$ 6 \div 2 = 3 $$
- Final prime factor
At this point, we have 3, which is a prime number. So we can stop here.
- 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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