n=27,916,924→2,791,684→279,160→27,916→
2,779→259→7
and so n is divisible by 7. Each time we run through the loop ofinstructions, we lose at least one digit, so the number ofpasses through the loop is about the same as the length of the number with which we begin.
To test whether or not nhas a factor of 11, subtract the final digit from the remaining truncated number and repeat. For example,the next number is a multiple of11 as our method reveals: