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Answering me this question please!!!
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Answer:
51,9
Step-by-step explanation:
Let the divisor be 'n'.
Given that Quotient is 6 more than five times the divisor.
Quotient = 5n + 6.
∴ Dividend = Divisor * Quotient + Remainder
⇒ 460 = n(5n + 6) + 1
⇒ 460 = 5n² + 6n + 1
⇒ 5n² + 6n - 459 = 0
⇒ 5n² - 45n + 51n - 459 = 0
⇒ 5n(n - 9) + 51(n - 9) = 0
⇒ (5n + 51)(n - 9) = 0
⇒ n = 9, -51/5{∵neglected}
⇒ n = 9.
When n = 9:
Quotient = 5n + 6 = 51.
Therefore:
Quotient = 51, Divisor = 9.
Hope it helps!
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