Greatest common factor is a common factor shared by two or more numbers.  is a multiple of , so let's divide  for both numbers. We get . We are finished as these are the basic numbers. So the greatest common factor is .

Greatest common factor is a common factor shared by two or more numbers.  is a prime number.  is a composite number. Since we have a prime and composite number, the greatest common factor is . 

Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide two for both numbers. We get .  We have  one prime and one composite number, so we are finished. The greatest common factor is .

Greatest common factor is a common factor shared by two or more numbers. If you know the divisibility rule of  (sum of digits are divisible by ), then the answer is just  as the quotient is . We have a prime and composite number. However, if you don't and only know the divisibility rule of , then we can divide both numbers by  to get . We do it once more to get . Since we divided twice by , we multiply these factors and this is our greatest common factor of . Our answer is .

Greatest common factor is a common factor shared by two or more numbers. If you know divisibility rule of , then this is the answer. However, this isn't easy to spot, so we will do process of elimination. The numbers are odd and if we have even factors, we never generate odd numbers so  is wrong. Next, check divisibility rule of . The digits of  add to  which isn't divisible by  so  is wrong. Next, let's divide  into . We get a decimal value and that's wrong since if we consider  to be a multiple of , it should be a whole number and not a decimal. Finally, by dividing  and , it's also . This is our answer. To find out if  is divisible by , just add the outside digits and match the middle one. Since it does,  is divisible by .

These two numbers are definitely divisible by . When we divide both numbers by , we get  and  remaining. Since we have a combination of a prime and composite number, then we can't find any more factors. Our answer is .

Let's do some divisibility rules. For , the sum of the digits must be divisible by .

We have:

 They are both good so when we divide both numbers by , we get . Lastly they are both divisible by . So we multiply both factors to get an answer of .

Greatest common factor involves all the numbers in the set. Even though three of the numbers are divisble by ,  isn't. The only factor that satisfies all the numbers is . 

Although the first three numbers are divisible by ,  doesn't divide evenly into . The next best factor is . The remainder will be . This won't go any further as most of the numbers are even except . Our final answer is just .

We know all of the numbers are divisible by  so when we divide all the numbers by , we have . Next, we can divide al of them by , because the sum of the digits of all numbers are divisible by . So we get . This is as best as we can go so now we multiply the factors to get  as an answer.