Question

The largest number which divides 77, 147, and 252 leaving the same remainder in each case: a) 9 b)15 c)25 d) 35

Answer 1

reqd number = H.C.F. of (147-77)
(252-147) and (252-77)
= H.C.F. of 70,105 and 175
= 35
( 70 = 2✘5✘7, 105 = 5✘3✘7 and 175=5✘5✘7 )
H.C.F. =5✘7 = 35

Answer 2

required number = HCF of { b-a, c -b, c -a}

so,
HCF of { (147-77) , (252-147), (252-77)}
={ 70 , 105 , 175 }

factor of 70 = 2× 5 × 7
factors of 105 = 5 × 7 ×3
factors of 175 = 5 × 7 × 3

so, common factors of all = 35

so, 35 is the answer