The prime factorization of 81 is 3 x 3 x 3 x 3, or 3 ^ 4. Prime factorization of a number involves finding the prime numbers that, when multiplied together, yield that number.
A prime number is a number that is divisible only by itself and one. Neither zero nor one is considered a prime number. To complete prime factorization on 81, find a common pair of dividends that multiplied together equal 81. Nine times nine equals 81, but nine is not a prime number because it is divisible by three. Break down each nine into three times three. Three is a prime number since only three and one are factors of it. Three times three times three times three is equal to 81.