If 3214 is divided by 234 and leaves a remainder r, what is the value of r?
-
A.
zero -
B.
1 -
C.
2 -
D.
3
Correct Answer: Option C
Explanation
(frac{321_4}{23_4}\=frac{(3times4^{2})+(2times4^{1})+(1times4^{0})}{(2times4^{0})+(3times4^{0})}\=frac{3times16+2times4+1times1}{2times4+3times1}\=frac{48+8+1}{8+3}\=frac{57}{11}=5hspace{1mm}remainderhspace{1mm}2\∴r=2_{10} \ Nowhspace{1mm}converthspace{1mm}2_{10} hspace{1mm}tohspace{1mm}basehspace{1mm}4\frac{4}{2} = 2\frac{4}{0}=0hspace{1mm}orhspace{1mm}2\∴r=2)