Do you know division?
Number Theory
Level
3
An integer, when divided by a divisor, leaves a remainder of 27. Twice the same integer divided by the same divisor leaves a remainder of 3. What is the value of the divisor?
The answer is 51.
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1 solution
Let 'N' be the divident 'D' be the divisor and 'a' and 'b' be any arbitrary constants . From statement-1 we get N = aD + 27 and D > 27 (since divisor is always greater than remainder) . From statement-2 we get N = bD + 3 . Equating them we get ,
2aD + 54 = bD +3 ,
2aD + 51 = bD ,
For this to happen 51 has to be a multiple of 'D' , thus it could be any of 1,3,17,51 but since we already know D > 27 , Hence
D= 51