Dividing by 8

Tuesday, January 12, 2010

Check the last three digits. Since 1000 is divisible by 8, if the last three digits of a number are divisible by 8, then so is the whole number. Example: 33333888 is divisible by 8; 33333886 isn't. How can you tell whether the last three digits are divisible by 8? Phillip McReynolds answers: If the first digit is even, the number is divisible by 8 if the last two digits are. If the first digit is odd, subtract 4 from the last two digits; the number will be divisible by 8 if the resulting last two digits are. So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8. 33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.

Sara Heikali explains this test of divisibility by eight for numbers with three or more digits:

1. Write down the units digit of the original number.
2. Take the other numbers to the left of the last digit,
and multiply them by two.
3. Add the answer from step two to the number from step one.
4. If the sum from step three is divisible by eight, then the 
original number is divisible by eight, as well. If the sum is 
not divisible by eight, then the original number is not 
divisible by eight.

For example, if the number we are testing is 104, then
1. Write down just the digits in ones place: 4.
2. Take the other numbers to the left of that last digit,
and multiply them by two: 10 × 2 = 20.
3. Add the answer from step two to the number from step one:
4 + 20 = 24.
4. Twenty-four is divisible be eight. Therefore, our original
number, one hundred and four, is also divisible by eight.