Question

What is the largest number which divides $1475,3155$ and $5255$ leaves the same remainder in each case

• A. $320$
• B. $420$
• C. $350$
• D. $410$

Answer 1

The correct option is B $420$

Take the relative difference of given numbers

$3155-1475=1680$

$5255-3155=2100$

$5255-1475=3780$

$1680=2\times 2\times 2\times 2\times 3\times 5\times 7$

$2100=2\times 2\times 3\times 5\times 5\times 7$

$3780=2\times 2\times 3\times 3\times 3\times 5\times 7$

H.C.F of $1680,2100,3780=2\times 2\times 3\times 5\times 7=420$

Hence, the largest number is $420$.