Let us develop a general divisibility criterion that proceeds recursively. Suppose that n is given in decimal n = (akak-1...a1a0) base 10. Let d 22 be any positive integer with gcd(d, 10) = 1. Let e = N be a multiplicative inverse of 10 modulo d. Define n'=(n-a0 )/10 +e *a0. Prove that d | n if and only if d | n'. Thus, we can determine whether n is divisible by d by constructing the sequence n, n' (n')'.... until we reach a term small enough that we can tell whether it is divisible by d.