Number Theory Problem
Number Theory
Level
3
Find the smallest natural number which has the following properties : 1)It's decimal representation has 6 as the last digit. 2)If the last digit is erased and placed in front of the remaining digits the resulting number is four times as large as the original number.
The answer is 153846.
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1 solution
As the new number starts with a 6 and the old number is 1/4 of the new number, the old number must start with a 1.
As the new number now starts with 61, the old number must start with 61/4= 15.25
We continue in this way until the process terminates with the new number 615,384 and the old number =153846