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No. All the multiples of 4 are even numbers.
There is not any kind of overall religious prohibition on who views the X Factor. Whether or not someone can view the show would be a personal or family decision.
There is only one proper common factor of 12 and 38; it is 2. Mathematicians do not consider 1 to be a proper factor, because it divides everything.
Exponents are just the number of times a factor is repeated. Consider 64. 64 32,2 16,2,2 8,2,2,2 4,2,2,2,2 2,2,2,2,2,2 There are six twos. That's 26
Technically, 7 is a prime number so itself and 1 are the only candidates. If you consider 1 to be a factor, then the only common factor is 1, which is not useful in any application I know.