Prime factor of 455
Understand the Problem
The question is asking for the prime factorization of the number 455. To solve it, we will find the prime numbers that multiply together to give 455.
Answer
The prime factorization of 455 is $5 \times 7 \times 13$.
Answer for screen readers
The prime factorization of 455 is $5 \times 7 \times 13$.
Steps to Solve
- Start with the smallest prime number
Begin by checking if 455 is divisible by 2. Since 455 is an odd number, it is not divisible by 2.
- Check divisibility by the next prime number (3)
Next, check if 455 is divisible by 3 by adding the digits (4 + 5 + 5 = 14) and seeing if the sum is divisible by 3. Since 14 is not divisible by 3, 455 is also not divisible by 3.
- Check divisibility by the next prime number (5)
Now check divisibility by 5. Since 455 ends in 5, it is divisible by 5. So we will divide 455 by 5:
$$ 455 \div 5 = 91 $$
- Factor the resulting number (91)
Now we need to factor 91. We'll check divisibility by the next smallest prime number, which is 7:
$$ 91 \div 7 = 13 $$
- Combine the prime factors
Now we have found all prime factors. So, we can write the prime factorization of 455 as:
$$ 455 = 5 \times 7 \times 13 $$
The prime factorization of 455 is $5 \times 7 \times 13$.
More Information
The number 455 is a product of three prime numbers: 5, 7, and 13. Recognizing the characteristics of prime numbers is essential in the process.
Tips
- Miscalculating divisibility tests, especially for small primes like 3 or 7. Always check carefully if a number divides evenly.
- Forgetting to check all relevant prime numbers can lead to incomplete factorization.