How do you write the prime factorization of 81?

To find the prime factorization of 81, you need to break it down into its prime factors. Here’s how you can do it:

Step-by-Step Process

1. **Start with the number**: Begin with 81.

2. **Divide by the smallest prime number**: The smallest prime number is 2, but since 81 is odd, we move to the next prime, which is 3.

3. **Perform the division**: Divide 81 by 3.

• 81 ÷ 3 = 27

4. **Repeat the process**: Now take 27 and divide it by 3 again.

• 27 ÷ 3 = 9

5. **Continue dividing**: Next, divide 9 by 3.

• 9 ÷ 3 = 3

6. **Final division**: Finally, divide 3 by 3.

• 3 ÷ 3 = 1

Result

Now that you have divided down to 1, you can write the prime factorization. Since you divided by 3 four times, the prime factorization of 81 is:

This means that 81 can be expressed as 3 raised to the power of 4.