What are the prime factors of 330?
Understand the Problem
The question is asking for the prime factors of the number 330. To solve this, we need to find the prime numbers that multiply together to produce 330.
Answer
The prime factors of 330 are $2$, $3$, $5$, and $11$.
Answer for screen readers
The prime factors of 330 are $2$, $3$, $5$, and $11$.
Steps to Solve
- Start with the number 330
Begin by analyzing the number 330 to identify its factors.
- Divide by the smallest prime number
Check if 2, the smallest prime number, can divide 330. Since 330 is even, we can divide: $$ 330 \div 2 = 165 $$
So, 2 is a prime factor.
- Check the next prime number
Now, we need to factor 165. The next smallest prime number is 3. Check if 3 can divide 165: $$ 165 \div 3 = 55 $$
Thus, 3 is another prime factor.
- Continue factoring with next prime numbers
Now, factor 55. The next prime number is 5. Since 55 ends in 5, we can divide: $$ 55 \div 5 = 11 $$
So, 5 is also a prime factor.
- Identify the last factor
Now we have 11. Check if 11 is a prime number. It only has two factors: 1 and itself, so it is prime.
- Combine all the prime factors
Now we have all the prime factors of 330: $$ 330 = 2 \times 3 \times 5 \times 11 $$
The prime factors of 330 are $2$, $3$, $5$, and $11$.
More Information
The number 330 is interesting because it is the product of the first four prime numbers. Prime factorization is a fundamental concept used in various fields in mathematics, including number theory and cryptography.
Tips
- Skipping prime checks: Sometimes, one might forget to check all prime numbers in order. Always start with the smallest prime and move upwards.
- Forgetting that 1 is not a prime number: Be careful to remember that 1 is not considered a prime.