Question

Find the largest number which divides 55, 127 and 175 so as to leave the same remainder in each case

• A. $24$
• B. $20$
• C. $21$
• D. $25$

Answer 1

The correct option is A $24$

Since the remainders are the same the difference of every pair of given numbers would be exactly divisible by
the required number
127 - 55 = 72, 175 - 127 = 48, 175 - 55 = 120
$\therefore$ Required number = HCF of 72, 48 and 120
$72=2^3\times 3^2,48=2^4\times 3,120=2^3\times 3\times 5$
Therefore the required number is$=2^3\times 3=8\times 3=24$