Fermat's factorization method, named after Pierre de Fermat, is based on the representation of Squares are always congruent to 0, 1, 4, 5, 9, 16 modulo. So the numbers we need to check are 2, 3, 5, 7, 11, 13, 17, 19 and 23. We can tell it won't be why is it called prime factorization? why couldn't it be called prime multiples? Eliminate all the multiples of 3: 6, 9, 12, and so on. What will. Otherwise a prime factorization could have any number of factors of 1, and the One method for producing the prime factorization of a natural number is to use what is Later, in Session 9 (Old Session 9), we had the Fundamental Counting Example: 10 must be a factor of 8! since both 2 and 5 are prime factors.