The greatest number will divide 38 and 68 leaving remainder 8 every time.?

=>  38 -  8 = 30

= 53 - 8 =  45

now lets find the hcf of 30 and 45

factors of 30 = 1,2,3,5,6,15,10,30

factors of 45 = 1, 3, 5, 9, 15 and 45.

so hcf

=>15

hence 15 is the greatest number that divides 38 and 53 leaving 8 as remainder in each case.

 

=  38 -  8 = 30
=  68 -  8 = 60
Now we have to find the hcf of 30 and 60 and that will be 30. Below is the calculation          
30)60(2
   60
   ===
    0
   ===                   

 

Dear Ritvik,

Since every time on dividing 38 and 68 remainders will be 8, hence first subtract 8 from the dividends which are 38 and 68.

Now the dividends are 30 and 60.

To find the highest number which divides them we need to find the h.c.f of the two.

H.C.F(30,60) = 30

Hence the answer is 30!!

Hope it helps!

regards,

Soumendu Majumdar