how you get the common factor of a mixed number

Question

68/646=2/19  common factor is 34, how you get it ?

Answer 1

Break down each mumber into its factors, start with 2 try the prime nos 2,3,5,7,11,13,17,19,23 ......

68= 2 x 34=2x 2x 17

646= 2 x 323= 2x17x19

common between them is 17 and 2 i.e.34

Answer 2

In this question you are trying to find a factor that can be divided into both the numerator and denominator in order to simplify the faction. Both the numerator and denominator can be divided by 34. Once you divide both sides by 34 you will end up with 2/19. 

68 divided by 34 equals 2

646 divided by 34 equals 19 

You can work backwards in order to find the common factor. To do this

68 divided by 2 = 34

646 divided by 19 =34