What is the prime factorization of 273?
Understand the Problem
The question is asking for the prime factorization of the number 273, which involves breaking it down into its prime number factors.
Answer
The prime factorization of 273 is $3 \times 7 \times 13$.
Answer for screen readers
The prime factorization of 273 is $3 \times 7 \times 13$.
Steps to Solve
- Start with the number 273
We'll begin by dividing 273 by the smallest prime number, which is 2. Since 273 is odd, it is not divisible by 2.
- Check divisibility by 3
Next, we'll check if 273 is divisible by 3. We can do this by adding the digits: $2 + 7 + 3 = 12$, which is divisible by 3. Now we divide:
$$ 273 \div 3 = 91 $$
- Factor 91
Now we need to factor 91. We'll check divisibility by the next smallest prime number which is 5. Since 91 does not end in 0 or 5, we move to the next prime, which is 7.
We'll check 91 for divisibility by 7:
$$ 91 \div 7 = 13 $$
- Identify all factors
We find that 91 factors into 7 and 13.
At this point, we have:
$$ 273 = 3 \times 7 \times 13 $$
- Check for primes
Finally, we check if 3, 7, and 13 are all prime numbers. Since they are, we have completed the factorization process.
The prime factorization of 273 is $3 \times 7 \times 13$.
More Information
273 is an interesting number as it is the product of three prime factors. The prime factors, 3, 7, and 13, are all relatively small and can be easily verified through basic division.
Tips
- Forgetting to check if numbers are prime: Ensure each quotient is examined to confirm its primality.
- Miscalculating division: Double-check calculations to avoid errors in the factors.
