The prime factors of 45 are three, three and five. These three numbers represent the unique combination of prime numbers that, when multiplied together, produce 45 as an answer.
According to About.com, a prime number is a whole number that is larger than one and cannot be divided evenly by any numbers other than one and the number itself. Zero and one are not considered prime numbers, but two, three, five and seven are. A number such as six is considered a composite number and not a prime number because it can be divided by two and three.
A common method used for finding prime factors of a number is to create a prime factorization tree.