prime factorization of 495
Understand the Problem
The question is asking for the prime factors of the number 495. We will approach this by dividing 495 by the smallest prime numbers until we reach 1.
Answer
The prime factorization of 495 is $3^2 \times 5 \times 11$.
Answer for screen readers
The prime factorization of 495 is $3^2 \times 5 \times 11$.
Steps to Solve
- Start with the number 495
We begin by identifying the smallest prime number, which is 2. Since 495 is odd, it is not divisible by 2.
- Check divisibility by the next prime, 3
Next, we check if 495 is divisible by 3. The rule for divisibility by 3 is that the sum of the digits must be divisible by 3.
Calculating the sum of the digits:
$$ 4 + 9 + 5 = 18 $$
Since 18 is divisible by 3, we divide:
$$ 495 \div 3 = 165 $$
- Continue with 165
Now we check 165 for divisibility by 3 again:
$$ 1 + 6 + 5 = 12 $$
Since 12 is also divisible by 3:
$$ 165 \div 3 = 55 $$
- Now check 55 for divisibility by the next prime, 5
55 ends with a 5, meaning it is divisible by 5:
$$ 55 \div 5 = 11 $$
- Finally, check the last number, 11
The number 11 is a prime number. Therefore, we cannot divide it further.
- Compile the prime factors
The prime factors we found are 3, 3, 5, and 11. We can express this as:
$$ 495 = 3^2 \times 5 \times 11 $$
The prime factorization of 495 is $3^2 \times 5 \times 11$.
More Information
The prime factorization of numbers helps in several areas of mathematics, including finding the greatest common divisor (GCD) and least common multiple (LCM). Additionally, prime factorization plays a crucial role in number theory and cryptography.
Tips
- Forgetting to check for divisibility by other small primes like 3, which can lead to missing factors.
- Confusing prime number definitions; it’s important to remember that a prime number has only two distinct positive divisors: 1 and itself.
