The prime factor of 81 is 3^4. A prime number is a number greater than one that is evenly divisible only by itself and one. A composite number, such as 81, is a number that has factors other than itself and one.
To find the prime factorization of 81, take two numbers that multiply together to make 81, such as 9 x 9. Nine is a composite number that is further broken down into 3 x 3. Break down both nines in this manner. Three is a prime number, so the prime factorization of 81 is 3 x 3 x 3 x 3, or 3^4.