What is the prime factorization of 184?
Understand the Problem
The question is asking for the prime factorization of the number 184, which involves determining the prime numbers that multiply together to give 184.
Answer
The prime factorization of 184 is $2^3 \times 23$.
Answer for screen readers
The prime factorization of 184 is $2^3 \times 23$.
Steps to Solve
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Start with the smallest prime number
Begin by dividing 184 by the smallest prime number, which is 2.
$$ 184 \div 2 = 92 $$ -
Continue dividing by 2
Next, take the result (92) and divide it by 2 again.
$$ 92 \div 2 = 46 $$ -
Divide by 2 once more
Repeat the process again with 46.
$$ 46 \div 2 = 23 $$ -
Identify the last prime factor
Now, check if 23 is a prime number. Since 23 has no divisors other than 1 and itself, it is a prime number. -
Write down the prime factorization
Combine the prime factors obtained from the divisions. The prime factorization of 184 is:
$$ 184 = 2^3 \times 23 $$
The prime factorization of 184 is $2^3 \times 23$.
More Information
Prime factorization is useful in various areas of mathematics, including simplifying fractions and finding the greatest common divisors. Additionally, every integer greater than 1 can be uniquely expressed as a product of prime numbers, which is called the Fundamental Theorem of Arithmetic.
Tips
- Stopping at non-prime numbers: Sometimes students may stop at a composite number instead of continuing until reaching prime factors. Always check if the resulting quotient is a prime number.
- Miscounting the factors: Be careful to count the number of times each prime divides the original number correctly.
