Of course the above scenario would never happen (we all carry around
calculators) but it’s good to know that if we should find ourselves in a similar
situation there is an easy divisibility rule for 67: remove the two rightmost
digits from the number (in our case, 53), double them (106) and subtract
that from the remaining digits (957335−106 = 957229); the original number
is divisible by 67 if and only if the resulting number is divisible by 67. If the
resulting number is not obviously divisible by 67 we can repeat the process
until we get a number that clearly is or is not a multiple of 67. In the above
example, we get the following.