What is the dvisibility rule for 7?

Answer 1

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the remaining digits of the number.

If the result is divisible by 7 (including zero), then the original number is divisible by seven. If the new number is still too big, you can apply the rule again.

Example: 406.

First, double the last digit, 6. (6 times 2 equals 12.)

Second, subtract that number from the remaining digits. (12 subtracted from 40 equals 28.)

Third, if the result is divisible by seven, the whole number is. (7 divides equally into 28.)

Thus, since the result is divisible by seven, we can conclude that 406 is divisible by seven.

If the result is still to big, repeat this procedure.

Example: 7,805.

Double the last digit, (makes 10,) subtract it from remaining digits, (780 minus 10 equals 770.)

770 is still to big a number to easily determine whether it is divisible by seven, so it is best to repeat the procedure, like so:

Double the last digit, which is a little weird since the last digit is zero, but 0 plus 0 still equals zero. (0 times 2 equals zero.) Subtract from remaining digits, (77 minus 0 equals 77.)

77 is divisible by 7, so we can conclude that 7,805 is divisible by seven.