Division Rule for 7

[mathgeek37]

By the way, Wikipedia's Divisibility Rule article has a concise description on why the Divisibility by 7 methods work.

Nice video.

[mathgeek37]

There is a simpler method...

Cast off the number in the ones places and then subtract the double of the cast off digit from the new number and repeat until you have a multiple of 7.

For example....999999

99999 - 18 = 99981

9998 - 2 = 9996

999 - 12 = 987

98 - 14 = 84

8 - 8 = 0

It works because 50 is congruent to 1 (mod 7). It has something to do with the fact 5 + 2 = 7. The other way to write the rule is to cast off the last digit and 5 times the digit to the remaining number.