Test for divisibility by 7

I mentioned this is class but didn't explain it.
Most people know that if a number ends in 5 or 0 it is divisible by 5
and
if it ends in an even digit it is divisible by 2
and
if you add the digits together and get a multiple of 3 then the original number is divisible by 3

for example:
4752 is divisible by 3 since 4+7+5+2 = 18 and 3 goes into 18

so, the test for 7...
take the ones digit and double it, subtract that number from the number formed by the remaining digits

example: 1603 is divisible bt 7 since 3*2 = 6 and 160 - 6 = 154
and
4*2 = 8 and 15 - 8 = 7

if you get zero, that counts too

like 84 - 4*2 = 8, 8 - 8 = 0

and the converse is true if you subtract and don't get 7 or 0 then your original number is not a multiple of 7