How do you find the greatest common factor of 30135 using prime factorization?

You do not. To have a greatest common factor, you need two or more numbers. A common factor is a factor that two or more number have in common.

However, the prime factorization of all the numbers will help you find the greatest common factor. The greatest common factor will be the prime factors they have in common multiplied together.

Example:

The prime factorization of 30135 is 3 x 5 x 7 x 7 x 41.

The prime factorization of 98 is 2 x 7 x 7.

The prime factors they have in common are 7 and 7, so the greatest common factor is 7 x 7 = 49.