No. The smallest coefficient possible is 1, and the smallest GCF is also 1. You cannot have a common factor of zero.
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the smaller number
There is no such thing as the smallest common factor. I guess the smallest common factor (integers only) for 16 and 24 would be -8. But that's just the negative version of the greatest common factor. I think you meant to ask either what is the smallest common multiple of 16 and 24 or what is the greatest common factor of 16 and 24. The greatest common factor of 16 and 24 is 8. The smallest common multiple of 16 and 24 is 48.
In the list of common factors, the greatest is the largest, the least is the smallest (which is always 1)
The smallest of the two numbers could be 850.
To split things into smaller sections.