Lowest Term Calculator

The lowest term (or simplest form) of a fraction is when the numerator and denominator share no common factor greater than 1. For example, 3/4 is the lowest term of 9/12, because dividing both by their GCF of 3 gives 3/4.

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, to simplify 18/24, the GCD is 6, so 18÷6 = 3 and 24÷6 = 4, giving the lowest term 3/4.

A fraction is in lowest terms when the only common factor between the numerator and denominator is 1. For example, 3/7, 5/8, and 11/13 are all in lowest terms. A fraction like 6/9 is not, because both share a common factor of 3.

The GCD of 4 and 20 is 4. Dividing both by 4 gives 1/5, so the lowest term of 4/20 is 1/5.

The GCD of 3 and 16 is 1, which means 3/16 is already in its lowest terms — there is no common factor greater than 1 to divide by.

An improper fraction has a numerator larger than its denominator, such as 9/4. When simplified, it can also be expressed as a mixed number — 9/4 becomes 2 and 1/4. This calculator shows both the simplified improper fraction and its mixed number form.

The Euclidean algorithm finds the GCD by repeatedly replacing the larger number with the remainder of dividing the two numbers until the remainder is 0. The last non-zero remainder is the GCD. For example, GCD(18, 24): 24 mod 18 = 6, then 18 mod 6 = 0, so GCD = 6.

Yes. Negative fractions follow the same simplification rules — the GCD is always positive, and the negative sign is preserved on the numerator. For very large numbers, the Euclidean algorithm still works correctly and efficiently.