You wouldn't normally list it in a factor tree, because it's not technically a Prime number, and besides if you did, you could keep on adding x1 x1 x1 x1 forever and not change the value.
That being said, if you wanted to show the factorization of a prime number, you'd most likely write it as (for example) 709 x 1, just to show that nothing else divides evenly into 709.
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Yes, just as 1 is considered a factor of everything, a number is considered a factor of itself.
Yes.
The least common factor of any set of integers is 1.
It is a conversion factor but, it could be considered a rate [of conversion].
If the number 1 is considered a factor, then these are the prime numbers. Their only factors are 1 and themselves.