If 321

_{4}is divided by 23_{4}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)