tncy work dione.1f460 is divided by a natural number, quotient is 6 mo

1.	tncy work dione.1f460 is divided by a natural number, quotient is 6 more than five times the divisand remainder is 1. Find quotient gnd diviser
Answer» Using Remainder theorem: 460 = Divisor x Quotient + Remainder Let divisor be D, quotient be Q, and Remainder is given 1 So, 460 = Q.D + 1 Q.D = 459.....(1) Now we have, Q = 5D + 6....(2) Solving (1) and (2) we get Q = 459/D Putting this in (2) we get 459/D = 5D + 6 459 = 5D² + 6D 5D² + 6D -459 = 0 5D² - 45D + 51D -459 = 0 5D(D - 9) + 51(D - 9) = 0 (5D + 51)(D - 9) = 0 D = 9 or -51/5 As it is given that divisor is natural number, D will only be 9 Divisor = 9 Quotient = 459/9 = 51

tncy work dione.1f460 is divided by a natural number, quotient is 6 more than five times the divisand remainder is 1. Find quotient gnd diviser

Answer»

Using Remainder theorem:

460 = Divisor x Quotient + Remainder

Let divisor be D, quotient be Q, and Remainder is given 1

So,

460 = Q.D + 1

Q.D = 459.....(1)

Now we have,

Q = 5D + 6....(2)

Solving (1) and (2) we get

Q = 459/D

Putting this in (2) we get

459/D = 5D + 6

459 = 5D² + 6D

5D² + 6D -459 = 0

5D² - 45D + 51D -459 = 0

5D(D - 9) + 51(D - 9) = 0

(5D + 51)(D - 9) = 0

D = 9 or -51/5

As it is given that divisor is natural number, D will only be 9

Divisor = 9

Quotient = 459/9 = 51