Question

5075,3584,2732 are divided by greatest number 'd', the remainder in each case is 'r', then (3d-2r)=​

Answer 1

The greatest number that will divide x, y and z leaving the same remainder in each case is = HCF of (x - y), (y - z) and (z - x).

So, difference between given numbers is:

⇒ 3584 - 2732 = 852

⇒ 5075 - 3584 = 1491

⇒ 5075 - 2732 = 2343

Then, Prime factors of 852, 1491 and 2343 are:

⇒ 852 = 2 * 2 * 3 * 71

⇒ 1491 = 3 * 7 * 71

⇒ 2343 = 3 * 11 * 71

HCF = 3 * 71 = 213 = d

∴ Remainder in each case is:

⇒ 5075/213 = 176 = r

⇒ 3584/213 = 176 = r

⇒ 2732/213 = 176 = r

Hence, (3d - 2r)

⇒ 3*213 - 2*176

⇒ 639 - 352

⇒ 287