In base 6 you may only use the numbers 0, 1, 2, 3, 4, and 5. The number 6 becomes 10.

253%6=1, 253/6=42; 42%6=0, 42/6=7; 7%6=1, 7/6=1; 1%6=1, 1/6=0

Taking the answers of the modulus equations from right to left yields the correct representation of 253 in base 6: 1101.

To convert this back into base 10: 1*(6^0)+0*(6^1)+1*(6^2)+1*(6^3)=253.

253%6=1, 253/6=42; 42%6=0, 42/6=7; 7%6=1, 7/6=1; 1%6=1, 1/6=0

Taking the answers of the modulus equations from right to left yields the correct representation of 253 in base 6: 1101.

To convert this back into base 10: 1*(6^0)+0*(6^1)+1*(6^2)+1*(6^3)=253.