Question

write the prime factorization of 18. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Start with dividing by smallest prime

Divide 18 by 2 (the smallest prime number). $18\div2 = 9$.

Step2: Factor the quotient

Now factor 9. The smallest prime that divides 9 is 3. $9\div3 = 3$.

Step3: Factor again

Factor the new quotient 3. $3\div3 = 1$.

Step4: Write prime factors

The prime factors are 2, 3, and 3. Using exponents, 3 appears twice, so the prime factorization is $2\times3^{2}$.

Answer:

$2\cdot3^{2}$