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2 is the only prime factor of 64.
to factor (x2-16x+64), you need to find two number whose product is 64 and whose sum is 16. These two numbers are 8 and 8. (x2-16x+64)=(x-8)(x-8)
There cannot be a lowest common factor of just one number. To be common there need to be at least two numbers.
It is 4 because it's the highest common factor of both numbers
45 and 64 are not prime numbers because they both have more than two factors