Question

when 5075, 3584 and 2732 are divided by the greatest number d, the remainder in each case is r. Then what is the value of (3d-2r) ?​

Answer 1

Given :- when 5075, 3584 and 2732 are divided by the greatest number d, the remainder in each case is r. Then what is the value of (3d-2r) ?

Solution :-

we know that,

• 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 .

Than, 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.

Therefore,

→ 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 (Ans.)

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