What is the remainder when the base-$50$ integer $12345_{50}$ is divided by $48$? Write your answer in base $10$.

What is the remainder when the base-50  integer 12345 base50   is divided by 48? Write your answer in base 10.

 

Is 48 in base 50 or in base 10?

What is the remainder when the base-50  integer 12345 base50   is divided by 48base10? Write your answer in base 10.

 

It is simply

 

\(12345_{50}=(5+4*50+3*50^2+2*50^3+1*50^4) _{10}\\~\\ 5+4*50+3*50^2+2*50^3+1*50^4 \quad\mod{48}\\ =5+4*(-2)+3*(-2)^2+2*(-2)^3+1(-2)^4 \quad\mod{48}\\ =5-8+12-16+16 \quad\mod{48}\\ =9 \quad\mod{48}\\ \)

 

The remainder will be 9