What are the prime factors of 18?
Understand the Problem
The question is asking for the prime factors of 18, which involves identifying the prime numbers that multiply together to give the original number.
Answer
The prime factors of 18 are \(2\) and \(3\).
Answer for screen readers
The prime factors of 18 are (2) and (3).
Steps to Solve
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Start with the Number We begin with the number 18. Our goal is to break it down into its prime factors.
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Prime Factorization To find the prime factors, we can start dividing 18 by the smallest prime number, which is 2. $$ 18 ÷ 2 = 9 $$
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Continue with the Result Now we need to factor 9. The smallest prime number that can divide 9 is 3. $$ 9 ÷ 3 = 3 $$
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Final Division We see that the last result is also a prime number, which is 3. $$ 3 ÷ 3 = 1 $$
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List the Prime Factors Now, we can list all the prime factors that we used to reach 1:
- First division by 2
- Two divisions by 3
Therefore, the prime factorization of 18 is: $$ 18 = 2 × 3 × 3 $$ Or more concisely, $$ 18 = 2 × 3^2 $$
The prime factors of 18 are (2) and (3).
More Information
The prime factorization indicates that 18 can be expressed as a product of prime numbers, specifically (2) and (3). Since (3) appears twice, it is often written as (3^2). Understanding prime factorization helps in various areas of mathematics, including simplifying fractions and finding least common multiples.
Tips
One common mistake is forgetting to check for all prime factors or misclassifying a composite number as prime. To avoid this, always divide by the smallest available prime number and check each result.
