This result suffices to show that the number of steps in Euclid's algorithm can never be more than five times the number of its digits (base 10). For if the algorithm requires "N" steps, then "b" is greater than or equal to "F""N"+1 which in turn is greater than or equal to "φ""N"−1, where "φ" is the golden ratio. Since "b" ≥ "φ""N"−1, then "N" − 1 ≤ log"φ""b". Since log10"φ" > 1/5, ("N" − 1)/5 < log10"φ" log"φ""b" = log10"b". Thus, "N" ≤ 5 log10"b". Thus, the Euclidean algorithm always needs less than "O"("h") divisions, where "h" is the number of digits in the smaller number "b".