Euclid's algorithm to compute the greatest common divisor (GCD) to two numbers appears as Proposition II in Book VII ("Elementary Number Theory") of his "Elements". Euclid poses the problem thus: "Given two numbers not prime to one another, to find their greatest common measure". He defines "A number be a multitude composed of units": a counting number, a positive integer not including zero. To "measure" is to place a shorter measuring length "s" successively ("q" times) along longer length "l" until the remaining portion "r" is less than the shorter length "s". In modern words, remainder "r" = "l" − "q"×"s", "q" being the quotient, or remainder "r" is the "modulus", the integer-fractional part left over after the division.