Question

Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why? Give an example of how prime factorization could be used in the real world.

Answer 1

Prime factors are factors of a composite number that are indivisible except by the number 1 or the number itself. The answers to your questions are the following:

1. Yes, it is possible especially for very large numbers. 
2&3. No, because as mentioned previously, the default prime factors of numbers are 1 and the number itself. For example, 2 is a prime number. Its factors are 1 and 2.
4. Prime factorization are useful in fields of encryption. They make use of the basic prime numbers for the arithmetic modulus with the general equation: n=pq.