The prime factorization of 81 is 3 x 3 x 3 x 3, or more succinctly, 34.
To explain how we arrive at that, let’s start by dividing 81 by the smallest prime number, which is 3. When we divide 81 by 3, we get 27. Dividing 27 by 3 again gives us 9. Continuing this process, we divide 9 by 3 to get 3, and finally, we divide 3 by 3 to get 1. Each time we divide by 3, we’re finding a prime factor:
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Since we divided by 3 a total of four times, we can express the prime factorization of 81 as 34. This means that 81 can be written as the product of the prime number 3 multiplied by itself four times.