What is the prime factorization of 289?
Understand the Problem
The question is asking for the prime factorization of the number 289. This means we need to express 289 as a product of prime numbers.
Answer
The prime factorization of 289 is $17^2$.
Answer for screen readers
The prime factorization of 289 is $17^2$.
Steps to Solve
- Check if 289 is a perfect square
To start, we can check if 289 is a perfect square by taking the square root of 289.
$$ \sqrt{289} = 17 $$
Since 17 is an integer, this indicates that $289 = 17^2$.
- Express 289 as a product of primes
Since we determined that 289 is a perfect square, we can write it as:
$$ 289 = 17 \times 17 $$
Now, we see that 17 is a prime number.
- Final prime factorization
Consequently, the prime factorization of 289 can be written as:
$$ 289 = 17^2 $$
This means that the number 289 can be expressed as the product of the prime number 17, multiplied by itself.
The prime factorization of 289 is $17^2$.
More Information
The number 289 is interesting because it is the square of a prime number (17). It illustrates how square numbers can have repeated prime factors.
Tips
- Forgetting that a prime factorization means breaking it down into only prime numbers can lead to incorrect answers.
- Confusing the prime factorization with the expression of the number itself without recognizing it as a product.
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