question_answer

The greatest number that can divide 140,176,264 leaving remainders of 4,6, and 9 respectively is

A)  85                   

B)  34

C)  17                   

D)  2

Correct Answer: C

Solution :

[c] Required number \[=H.C.F\,\,of\,\,(140-4),\,\,(176-6)\]and of 136, 170 and 255. \[\therefore \] Required number =17 Alternate Method: Here divisible terms are \[140-4=136,\,\,176-6=170\] and \[264-\,9=255\] Now, difference between these numbers \[170-\,136=34\] \[225-\,170=85\] H.C.F of difference =17 Hence required number =17.