What are the prime factors of 184?
Understand the Problem
The question is asking for the prime factors of the number 184. This involves breaking down the number into the prime numbers that, when multiplied together, will give us the original number.
Answer
The prime factors of 184 are $2^3$ and $23$.
Answer for screen readers
The prime factors of 184 are $2^3$ and $23$.
Steps to Solve
- Start with the number 184
To find the prime factors of 184, we'll start by dividing it by the smallest prime number, which is 2.
- Divide by 2
Since 184 is even, we can divide it by 2: $$ 184 \div 2 = 92 $$
- Continue dividing by 2
Now, we take 92 and divide by 2 again: $$ 92 \div 2 = 46 $$
- Continue dividing by 2 once more
Next, we divide 46 by 2: $$ 46 \div 2 = 23 $$
- Check if 23 is prime
Now we have 23, which needs to be factored. To check if 23 is prime, we see that it cannot be divided evenly by any prime number less than its square root (approximately 4.8). The prime numbers to check are 2 and 3:
- 23 is not divisible by 2 (it’s odd).
- 23 is not divisible by 3 (the sum of digits is 5).
Since 23 is not divisible by any primes below its square root, it is a prime number.
- Write the prime factorization
Now, we can summarize the prime factorization of 184: $$ 184 = 2^3 \times 23 $$
The prime factors of 184 are $2^3$ and $23$.
More Information
The prime factorization shows how the number 184 can be expressed as a product of prime numbers. It's interesting to note that 2 is the only even prime number, and in this case, it factors into the number multiple times.
Tips
- Not recognizing that the process of dividing by 2 should continue until the result is no longer even.
- Incorrectly identifying whether a number is prime; remember to test divisibility only up to the square root of the number.
