### Instruction: Find $120_4\times13_4\div2_4$. Express your answer in base 4.### Response: Ok let's start by converting all of these numbers to base 10.
Sure. $120_4=1\cdot 4^2+2\cdot 4^1=16+8=24$.
$13_4=1\cdot 4^1+3\cdot 4^0=4+3=7$.
And $2_4=2\cdot 4^0=2$.
Now we just need to solve $24\times 7\div 2$.
Which is just $24\times 3.5=84$.
Right. Now we just need to convert this back to base 4.
Ok. The largest power of 4 that is less than or equal to 84 is $4^3=64$. The largest multiple of 64 that is less than or equal to 84 is $1\cdot 64$, so the first digit is 1.
Now we have 84-64=20 left. The largest power of 4 that is less than or equal to 20 is $4^2=16$. The largest multiple of 16 that is less than or equal to 20 is $1\cdot 16$, so the second digit is 1.
Now we have 20-16=4 left. The largest power of 4 that is less than or equal to 4 is $4^1=4$. The largest multiple of 4 that is less than or equal to 4 is $1\cdot 4$, so the third digit is 1.
Now we have 4-4=0 left. So the last digit is 0.
So $120_4\times13_4\div2_4=1110_4$.