Question

write the prime factorization of 96. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Divide by smallest prime

Divide 96 by 2: \( 96 \div 2 = 48 \)

Step2: Repeat division by 2

\( 48 \div 2 = 24 \)

Step3: Repeat division by 2

\( 24 \div 2 = 12 \)

Step4: Repeat division by 2

\( 12 \div 2 = 6 \)

Step5: Repeat division by 2

\( 6 \div 2 = 3 \)

Step6: Divide by next prime

Now divide 3 by 3: \( 3 \div 3 = 1 \)

Step7: Count exponents

We divided by 2 five times and by 3 once. So prime factorization is \( 2^5 \cdot 3 \)

Answer:

\( 2^5 \cdot 3 \)