Mathematics

If 3214 is divided by 234 and leaves a remainder r, what is the value…

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)