in a certain sum of dividend is 37693 the quotient and the remainder is greater than 52 but less than 104 find the divisor
Answers
given Dividend = 37693
quotient = 52
Remainder lies between 52 to 104
to get approximate Divisor, divide dividend by quotient
(37693)÷52=724.8(approx divisor)
Case1
if we take divisor=724
(37693)÷724,we get remainder 45 which falls below the given remainder range [52 to 104]
hence 724 can't be divisor
Case2
take divisor =723
(37693)÷723, we get remainder as 97...this 97 is in range of remainder specified..hence divisor is 723
Given : dividend is 37693, the quotient is 52and the remainder is greater than 52 but less than 104.
To Find : the divisor
Solution:
a=bq+r
a = dividend = 37693
b = divisor = ?
q = quotient = 52
r = remainder 52 < r < 104
0 ≤ r < b
52 < r < 104
=> 52 <52 +r' < 104
=> 0 < r' < 52
37693 = b(52) + 52 + r'
=> 37693 = (52)(b + 1) + r'
Taking 52 as Divisor , b + 1 will be Quotient as 0 < r' < 52
and b will be our required Divisor for initial condition
724
52 _| 37693 |_
364
_____
129
104
_____
253
208
_____
45
724 = b + 1
=> b = 723
Hence the divisor is 723
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