It can be fully reduced to lowest terms if both are divided by their greatest common divisor.
[5] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used.
The Euclidean algorithm is commonly preferred because it allows one to reduce fractions with numerators and denominators too large to be easily factored.
The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30.
As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets Which method is faster "by hand" depends on the fraction and the ease with which common factors are spotted.
could be represented as a ratio of integers, then it would have in particular the fully reduced representation a/b where a and b are the smallest possible; but given that a/b equals
In the case of rational functions the denominator could similarly be required to be a monic polynomial.