What are the prime factors of 18?
Understand the Problem
The question is asking for the prime factors of the number 18. To solve this, we need to find the prime numbers that multiply together to give the original number, which involves dividing 18 by prime numbers to identify those factors.
Answer
The prime factors of 18 are $2$ and $3$.
Answer for screen readers
The prime factors of 18 are $2$ and $3$ (with $3$ appearing twice).
Steps to Solve
- Identify the First Prime Number
Start with the smallest prime number, which is 2.
- Divide the Number by the Prime
Check if 18 is divisible by 2. Since $18 \div 2 = 9$, we can conclude that 2 is a prime factor.
- Continue with the Resulting Number
Now we have 9. We need to find the prime factors of 9. The next smallest prime number is 2, which does not divide 9, so we move to the next prime number, which is 3.
- Divide Again by the Next Prime Number
Check if 9 is divisible by 3. Since $9 \div 3 = 3$, we find that 3 is also a prime factor.
- Factor the Resulting Prime Again
We now have another 3 from the previous division, and since it is also prime, we can divide it again by 3.
- Finish the Factorization
$3 \div 3 = 1$. We cannot factor further as we reached 1. So far, we have $2$ and $3$ as factors.
- Write the Complete Factorization
The complete prime factorization of 18 is the product of the prime numbers: $$ 18 = 2 \times 3 \times 3 $$ or equivalently, $$ 18 = 2 \times 3^2 $$.
The prime factors of 18 are $2$ and $3$ (with $3$ appearing twice).
More Information
Prime factorization is a method to express a number as a product of its prime factors. The number 18 is interesting because it is the smallest composite number that can be factored into two distinct primes. The prime factors can also help in simplifying fractions and finding the least common multiples.
Tips
- Confusing composite numbers with prime numbers: Remember that prime numbers have only two distinct positive divisors: 1 and themselves.
- Not recognizing that factors can repeat: Remember that factors can occur more than once in a factorization, such as 3 in the case of 18.
