I have a conceptual question:
Does each positive integer have a unique combination of prime factors when we make its prime factorization?
In other words, when we calculate the prime factorization of a number, will we get always the same answer (combination)?, or there could be different sets of prime numbers (including repetitions) whose product is the same number?
For example, 100 = 2^2*5^2 , in this case is the only set of prime factors whose product is 100. However, I wonder whether in other numbers the opposite is possible.
Please, provide a detailed explanation.
Thanks!
Does each positive integer have a unique combination of prime factors when we make its prime factorization?
In other words, when we calculate the prime factorization of a number, will we get always the same answer (combination)?, or there could be different sets of prime numbers (including repetitions) whose product is the same number?
For example, 100 = 2^2*5^2 , in this case is the only set of prime factors whose product is 100. However, I wonder whether in other numbers the opposite is possible.
Please, provide a detailed explanation.
Thanks!
