# Lowest terms

A common fraction is in lowest terms if the numerator and denominator have no common factors other than 1. A fraction in lowest terms may also be said to be in simplest form.

Generally, it is good practice to present a solution involving fractions in lowest terms. A fraction in lowest terms is easier to read; while we may quickly recognize the fraction (which is in lowest terms) as the decimal 0.5, we would likely need to reduce to recognize it and being equivalent fractions.

## Reducing fractions to lowest terms

Reducing fractions to lowest terms is also referred to as simplifying them. There are a number of different ways to do this.

### Dividing by common factors

One of the most straightforward (but potentially tedious) ways to do this is to continue dividing the numerator and denominator by common factors until the only common factor is 1.

Example

Reduce the fraction to lowest terms.

54 is divisible by 2, but 81 is not, so we can try dividing the numerator and denominator by 3 instead.

Both 18 and 27 are also divisible by 3.

6 and 9 are also divisible by 3.

The only common factor of 2 and 3 is 1, so the fraction is now in simplest form. In this example, we had to divide a total of 3 times to arrive at a fraction in simplest form. The larger the number, the more tedious this method can get. If, however, we knew the greatest common factor between 54 and 81, we could've reduced this fraction in one step.

### Using the greatest common factor

The greatest common factor (GCF) method of reducing fractions is possibly the most efficient way to reduce a fraction, but involves knowing how to find the GCF of a set of numbers. Refer to the GCF page to learn how to find the GCF.

Once the GCF between the numerator and denominator of a common fraction is known, reducing the fraction just involves dividing the numerator and denominator by the GCF. In the example above, the GCF of 54 and 81, written GCF(54, 81), is 27. Thus, if we divide 54 and 81 by 27, we get the same result as we did above.

This method of reducing fractions is much quicker, but again requires knowledge of how to compute the GCF. Depending on the numbers involved, it is possible for the first method to be more efficient. With more experience, which method will be more efficient becomes more clear.