What is the prime factorization of 65?

The prime factorization of 65 is 5 x 13. Five and 13 are not just the only prime factors of 65, but they are also the only factors of this number other than 1 and 65. A prime number is one that has no factors other than itself and 1.

To find the prime factorization of a number, first write down all the factors of the number excluding 1 and the number itself. Next, factorize any nonprime factors into their prime factors. For example, the number 12 can be factorized as 3 x 4. To find the prime factorization of 12, one would then need to factorize 4 into its prime factors, which is 2 x 2. The prime factorization of 12 is therefore 2 x 2 x 3.