Question

find the largest no. which divides 248 and 1032 leaving remainder 8 in each case

Answer 1

for x is the factor of        248 - 8= 240  and 1032 - 8 = 1024                                      now take the lcm of their products  240=  2.2.2.2.3.5    and  1024=2.2.2.2.2.2.2.2.2.2                                                                                                hcf = 2.2.2.2=16                                                                                                            therefore 16 is the largest positive integer which divides 248 and 1032 leaving remainder 8 in each case.