1.4.1 Finding a Remainder when Dividing by 4, 8, etc…

Everybody knows that to see if a number is divisible by 2 you just have to look at the last digit, and if that is divisible by 2 (i.e. any even number) then the entire number is divisible by 2. Similarly, you can extend this principle to see if any integer is divisible by 4, 8, 16, etc…

For divisibility by 4 you look at the last two digits in the number, and if that is divisible by 4, then the entire number is divisible by 4.
With 8 it is the last three digits, and so on.

Let’s look at some examples:

123456 ÷ 4 has what remainder?
- Look at last two digits: $56 \div 4 = 14$ with remainder 0.
987654 ÷ 8 has what remainder?
- Look at last three digits: $654 \div 8 = 81$ with remainder 6.

Problem Set 1.4.1

364 \div 4 \text{ remainder}

1324354 \div 4 \text{ remainder}

246531 \div 8 \text{ remainder}

81736259 \div 4 \text{ remainder}

124680 \div 8 \text{ remainder}

214365 \div 8 \text{ remainder}

\text{Find } k \text{ so } 5318k \text{ is divisible by 8}