Double the last digit, subtract it from the rest. If the result is divisible by 7, the whole number is divisible by 7.
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Since 4 x 7 is 28, you know that 7 isn't a factor of 29. Since 29 is a prime number, you know that 7 isn't a factor of it. To be perfectly sure, divide 7 into 29. If the answer is an integer, it's a factor.
The only number that could be both a factor and a multiple is 7 itself.
Because 7 is a factor of 28 and 63 and 7 is a prime number.
The number 7 is a factor of 7,14,21,28,35,42,49,56,63,70,77,84,91,98,105 or anything multiplied by 7.
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.