Question

write the prime factorization of 42. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Start with the smallest prime

Divide 42 by the smallest prime number, 2. $42 \div 2 = 21$.

Step2: Factor the quotient

Now factor 21. The smallest prime that divides 21 is 3. $21 \div 3 = 7$.

Step3: Check the new quotient

7 is a prime number, so we stop here.

Step4: Write the prime factors

The prime factors of 42 are 2, 3, and 7. Since each prime factor appears once, we write the prime factorization as $2 \cdot 3 \cdot 7$.

Answer:

$2 \cdot 3 \cdot 7$