For comparison, Euclid's original subtraction-based algorithm can be much slower. A single integer division is equivalent to the quotient "q" number of subtractions. If the ratio of "a" and "b" is very large, the quotient is large and many subtractions will be required. On the other hand, it has been shown that the quotients are very likely to be small integers. The probability of a given quotient "q" is approximately ln|"u"/("u" − 1)| where "u" = ("q" + 1)2. For illustration, the probability of a quotient of 1, 2, 3, or 4 is roughly 41.5%, 17.0%, 9.3%, and 5.9%, respectively. Since the operation of subtraction is faster than division, particularly for large numbers, the subtraction-based Euclid's algorithm is competitive with the division-based version. This is exploited in the binary version of Euclid's algorithm.