How do you know if a number is divisible by 8?

Answer 1

There are 2 ways to do this.

Way 1:

Here's a simple way, based on the fact that 8 = 23; that is, 2 x 2 x 2.

Divide the number in question by 2 three times in a row. If you can divide it evenly by 2 each time (if every result is a whole number), then the number is evenly divisible by 8. If not, it's not. (Hint: Of course, if you start with or get to an odd number before the three divisions, it's not divisible evenly by 2, so you're done.)

Examples:

(1) Is 1,976 evenly divisible by 8?

1,976/2 = 988 (whole & even). 988/2 = 494 (whole & even). 494/2 = 247 (whole).

So 1,976 IS evenly divisible by 8.

(2) Is 2,444 evenly divisible by 8?

2,444/2 = 1,222 (whole & even). 1,222/2 = 611 (whole, but odd). You're done; 611/2 = 305.5 (fractional).

So 2,444 is NOT evenly divisible by 8!

Way 2:An alternative way is to divide the last three digits of a big number to see if it's divisible by 8. Example: 127398512

512 is divisible by 8.

It can be hard to memorize all the multiples of 8, so instead you can multiply the first digit by four and then subtract it from the last 2. I just found this out by messing around.

Example: 472

4 x 4 = 16

72 - 16 = 56

Since 56 is divisible by 8, 472, 23478, 23232324472, and7823728372472 are all divisible by 8.

If you subtract the product of the first digit and 4 from the last two digits and you get a negative number, divide the numbers riciprocal by 8. If the answer is rational, it works.

Example 512

4 x 4 = 20

12 - 20 = -8

riciprocal of -8 is 8

8/8 = 1

512 is divisible by 8.