Divisor Calculation Using Algorithm
The relationship between the dividend, divisor, quotient, and remainder is defined by the division algorithm:
$ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} $
Dividing 12401: Given Values
We are provided with the following information:
- Dividend = 12401
- Quotient = 76
- Remainder = 13
Let the unknown divisor be represented by 'D'. Substitute the known values into the division algorithm equation:
$ 12401 = (D \times 76) + 13 $
Quotient and Remainder Calculation
To find the divisor 'D', we first rearrange the equation to isolate the term containing 'D':
$ 12401 - 13 = D \times 76 $
Simplify the left side:
$ 12388 = D \times 76 $
Now, solve for 'D' by dividing 12388 by 76:
$ D = \frac{12388}{76} $
Performing the division calculation:
$ D = 163 $
Remainder Check and Final Divisor
The calculated divisor is 163. This result confirms the value needed when 12401 is divided by 163, yielding a quotient of 76 and a remainder of 13.
Similar Questions
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Important Questions from Divisibility and Remainder
If a five digit number 247xy is divisible by 3, 7 and 11, then what is the value of (2y - 8x)?
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- What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
