does the prime factorization using exponents and then add 1 to each exponent. then he find the product of these numbers.will this method work why or why not

The method you described is a way to find the total number of factors of a given number but not the actual prime factorization. Let me explain in more detail.

To find the prime factorization of a number, you need to express it as a product of its prime factors. For example, the prime factorization of 12 is 2^2 * 3^1 because 12 can be expressed as 2 * 2 * 3.

The method you mentioned, adding 1 to each exponent and then finding the product, gives you the total number of factors of a number. This is because when you add 1 to each exponent, you are essentially counting all the possible combinations of the prime factors. For example, in the case of 12, you have (2^0 * 3^0), (2^1 * 3^0), (2^2 * 3^0), (2^0 * 3^1), (2^1 * 3^1), (2^2 * 3^1). Multiplying all these combinations gives you the total number of factors, which in this case is 6.

So, to answer your question, this method can find the total number of factors of a number, but it does not give you the prime factorization itself. If you want to find the prime factorization, you need to identify the prime factors of the number and express them as exponents in the factorization.