Finding a Remainder when Dividing by 4, 8, etc...

To check for divisibility or find the remainder when dividing by powers of 2 (like 4, 8, 16, etc.), you only need to look at the last few digits of the number. For divisibility by $2^n$, you only need to examine the last $n$ digits of the number.

• Dividing by 4 ($2^2$): Look at the last two digits. The remainder of the original number is the same as the remainder of the last two digits divided by 4. Example: For 123456, check $56 \div 4$. The remainder is 0.
• Dividing by 8 ($2^3$): Look at the last three digits. The remainder of the original number is the same as the remainder of the last three digits divided by 8. Example: For 987654, check $654 \div 8$. The remainder is 6.