Find closest multiple of $117$ to $276$. We see that $2 \times 117 = 234$ is the nearest. Now subtract $234$ from $276$ to get reminder $42$. Add $2$ to quotient.
Find closest multiple of $117$ to $420$. We see that $3 \times 117 = 351$ is the nearest. Now subtract $351$ from $420$ to get reminder $69$. Add $3$ to quotient.
Since $69$ is less than $117$, stop the division. The reminder is $69$. The topmost line $0023$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $23$.