Find the prime factorization of 30.
Understand the Problem
The question is asking for the prime factors of the number 30, which means we need to determine the prime numbers that multiply together to give 30.
Answer
The prime factors of 30 are $2$, $3$, and $5$.
Answer for screen readers
The prime factors of 30 are $2$, $3$, and $5$.
Steps to Solve
- Start with the number 30
Identify the number you want to factor, which is 30.
- Find the smallest prime number
The smallest prime number is 2. Check if it divides 30 evenly:
$$ 30 \div 2 = 15 $$
Since this division yields a whole number, 2 is a prime factor of 30.
- Continue factoring the quotient
Now take the quotient, which is 15, and check for the next smallest prime number, which is still 2.
$$ 15 \div 2 $$
This does not yield a whole number, so we move to the next prime number, which is 3.
- Divide by 3
Now check 3:
$$ 15 \div 3 = 5 $$
Since this division also gives a whole number, 3 is another prime factor of 30.
- Check the quotient again
Now check the last quotient, which is 5. Since 5 is a prime number, this is the final prime factor.
- List the prime factors
The prime factors of 30 are the primes we found: 2, 3, and 5.
The prime factors of 30 are $2$, $3$, and $5$.
More Information
Prime factors are the prime numbers that multiply together to make a given number. In this case, 2, 3, and 5 multiply to give 30. This method of breaking down numbers helps in various mathematical concepts such as finding the greatest common divisor (GCD) or the least common multiple (LCM).
Tips
- Forgetting to check all prime numbers sequentially may lead to missing a factor.
- Stopping the process too early and not checking if the last quotient is a prime number itself.
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