1 is the factor that is common to all numbers.
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All non-zero whole numbers have factors. When you compare the lists of factors between two or more numbers, there will be numbers that are the same on both lists. Those are the common factors.
The common factor of every set of numbers is 1 because one is a factor of every number.
The greatest factor of any number is the number itself. There is no integer that is the greatest factor of every number. One is a factor of every number. One is the GCF of co-prime numbers.
By definition, every even number has 2 as a factor. That means that every set of even numbers will have at least 2 as a common factor. The GCF might be higher, but if it has 2 as a factor, it's even.
Every number has 1 as its factor and 1 is the smallest factor of any number. So least common factor of two or more numbers is always 1. Therefore, least common factor of 23 and 25 is 1.
If there is no factor that both of the numbers share (and there is not because they are both prime), then the answer is one. Every number has a factor of one, because every number times one is itself.
1 is a factor of every nonzero number, so 42 would have it in common with any other number.