Question

$N=(\mathrm{323232.......}50$ digits${)}_9.$ ie in base 9. Find the remainder when N is divided by 8?

• A. 1
• B. –1
• C. 0
• D. 3
• E. None of these

Answer 1

The correct option is D 3

In base 9, divisibility check for 8 is sum of the digits(digit sum) =Digit sum of $N=(25\ast 3+25\ast 2{)}_9=$

First convert the numbers to base 10

$25$ in base $10=23,$ Thus the question changes to $(23\ast 3+23\ast 2{)}_{10}={115}_{10}$

Converting it back to base 9 = 137, Now sum of digits in base $9=1+3+7=(4+7{)}_9=12\Rightarrow \frac{1+2}{8}{\mid }_R=3$