What is the prime factorization of 285?
Understand the Problem
The question is asking for the prime factorization of the number 285, which involves breaking it down into its prime components.
Answer
The prime factorization of 285 is $3 \times 5 \times 19$.
Answer for screen readers
The prime factorization of 285 is $3 \times 5 \times 19$.
Steps to Solve
- Start with the number 285
Begin the factorization process by checking divisibility by the smallest prime number, which is 2. Since 285 is odd, it is not divisible by 2.
- Check divisibility by the next smallest prime, 3
To check if 285 is divisible by 3, sum the digits (2 + 8 + 5 = 15). Since 15 is divisible by 3, we can divide:
$$ 285 \div 3 = 95 $$
- Factor the quotient, 95
Now we need to factor 95. First, check divisibility by 5 (the next prime). Since 95 ends in 5, it is divisible by 5:
$$ 95 \div 5 = 19 $$
- Check the final number, 19
Next, we check if 19 is a prime number. It has no divisors other than 1 and itself, so we stop here.
- Combine the factors
The prime factorization of 285 is thus the product of the prime factors we found:
$$ 285 = 3 \times 5 \times 19 $$
The prime factorization of 285 is $3 \times 5 \times 19$.
More Information
The prime factorization helps in understanding the structure of a number, which can be useful in various mathematical applications, including finding the greatest common divisor (GCD) or the least common multiple (LCM).
Tips
- Mistaking non-prime numbers for prime numbers. Always check if a number is prime by ensuring it has no divisors other than 1 and itself.
- Forgetting to check smaller primes before larger ones. It's important to start with the smallest primes.
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