Is the greatest common factor of any two odd numbers always odd
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Assuming you mean GCF and not GFC, the anwer is yes. If the
numbers are odd, neither can have an even factor and so there can
be no even common factor.
Yes.
Yes.
2 can never be a factor of an odd number and because of that it can’t be a common factor of any number pair where at least one of numbers is odd.