Question

Find the greatest number that will divide 55, 127, and 175, so as to leave the same remainder in each case.

(a) 1

(b) 16

(c) 24

(d) 15

Answer 1

Correct option : (c) 24

Difference between 127 - 55 = 72,

Difference between 175 - 127 = 48 and 

Difference between 175 - 55 = 120.

Required number should divided the differences between given numbers for leaving same remainder in each case.

Hence, Required number = HCF(72, 48, 120) = 24

\(\because\) \(72 = 24 \times 3\)

\(48 = 24 \times 2\)

\(120 = 24\times5\)