The prime factorization of 256 is two to the eighth power, or 2^8. The prime factors of a given number are the prime numbers that, when multiplied together, yield the given number. Prime numbers are numbers that are evenly divisible by only themselves and one.

To find the prime factors of 256, start by finding two numbers that multiply together to make 256, such as 8 and 32. Neither of these numbers is prime, so both must be further broken down into prime numbers. Eight equals four times two. Two is prime, but four is equal to two times two. Thirty-two equals eight times four. Eight is two times two times two, and four is two times two. Two, eight times, is the prime factor of 256.