To find the prime factorization of the number 18, we start by identifying the prime numbers that can multiply together to produce this number. Prime numbers are those greater than 1 that have no divisors other than 1 and themselves.
1. **Start with the smallest prime number, which is 2.** Since 18 is an even number, we can divide it by 2:
- 18 ÷ 2 = 9
2. **Next, we find the prime factors of 9.** The smallest prime number we can use to divide 9 is 3:
- 9 ÷ 3 = 3
3. **Now, we continue by dividing 3 by itself, since it is also a prime number:**
- 3 ÷ 3 = 1
Once we reach the number 1, we can conclude the factorization process. Now, we can summarize our findings:
18 can be expressed as:
- 18 = 2 × 3 × 3
- or, by using exponents, we can write it as: 18 = 2 × 3²
Thus, the prime factorization of 18 is 2 × 3².