What is the prime factorization of 18?
Understand the Problem
The question is asking for the prime factorization of the number 18, which involves breaking it down into the prime numbers that, when multiplied together, give the original number.
Answer
2 imes 3^2
Answer for screen readers
The prime factorization of 18 is 2 imes 3^2
Steps to Solve
- Find the smallest prime number that divides 18
Find the smallest prime number that can divide 18 without leaving a remainder. The smallest prime number is 2.
$$ 18 \div 2 = 9 $$
Now, 18 can be written as:
$$ 18 = 2 \times 9 $$
- Repeat the process for the resulting quotient (9)
Now we need to factorize 9. The smallest prime number that divides 9 is 3.
$$ 9 \div 3 = 3 $$
So, 9 can be written as:
$$ 9 = 3 \times 3 $$
- Combine the results
Now combine all the prime factors we found.
$$ 18 = 2 \times 3 \times 3 $$
Or, using exponentiation to simplify:
$$ 18 = 2 \times 3^2 $$
The prime factorization of 18 is 2 imes 3^2
More Information
Prime factorization helps in many areas of mathematics, including simplifying fractions and finding gcd (greatest common divisors) and lcm (least common multiples).
Tips
A common mistake is to forget to check for smaller prime numbers first (like starting with 3 instead of 2), which can lead to incorrect factorization.