Question 4 : Find the largest number which divides 64, 136 and 238 to leave the same remainder in each case.
Solution : To find the required number, we need to find the HCF of (136-64), (238-136) and (238-64), i.e., HCF (72, 102, 174).
72 = 2^{3} x 3^{2}
102 = 2 x 3 x 17
174 = 2 x 3 x 29
Therefore, HCF (72, 102, 174) = 2 x 3 = 6
hence, 6 is the required number.
why we find hcf of difference between pairs of number