Write the prime factorization of 9. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).Submit

Break Down the Problem

1. Identify what prime factorization is.
2. Determine the prime factors of the number 9.

Relevant Concepts

• Prime factorization involves expressing a number as the product of its prime factors.
• A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Analysis and Detail

1. Start with the number 9.
2. Divide 9 by the smallest prime number:
   • 9 ÷ 3 = 3
   • Since 3 is also a prime number, we can factor it further:
   • 3 ÷ 3 = 1
3. Therefore, the complete factorization of 9 using prime factors is:
   • $9 = 3 \times 3 = 3^2$

Verify and Summarize

• The calculation shows that we can express 9 as $3^2$.
• There are no other prime factors for the number 9.

Final Answer

The prime factorization of 9 is $3^2$.