If you are talking about the number itself, they can be the same.
To be specific:
A Prime number is a number that only has the factors 1 and itself.
A factor is a number that when multiplied creates a product.
A prime factor is a prime number that is multiplied to create a product.
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It depends how its used. 3 is a prime number. 3 is a prime factor of 12.
same number multiplied by one
Prime number refers to what they are; prime factor refers to what they do. A number doesn't become a factor until it is multiplied. 2 and 3 are prime numbers. 2 and 3 are prime factors of 6.
That's a prime factor.
13 is a prime number. The only prime factor of a prime number is the number itself.