Simplify Fractions Calculator

Reduce any fraction to its lowest terms with step-by-step prime factorization and GCD division.

Enter Your Fraction

Result

Simplified Fraction
2/3
lowest terms
GCD12
Numerator Factors2³ x 3
Denominator Factors2² x 3²
Decimal0.666667

Step-by-Step Solution

24/36 = (24 / 12) / (36 / 12) = 2/3

How to Simplify Fractions

Simplifying a fraction means reducing it to its lowest terms so that the numerator and denominator share no common factors other than 1. This is done by dividing both the numerator and denominator by their Greatest Common Divisor (GCD).

Step-by-Step Method

  1. Find the prime factorization of both the numerator and denominator.
  2. Identify the common prime factors.
  3. Compute the GCD by multiplying all common prime factors.
  4. Divide both numerator and denominator by the GCD.

Examples

12/18

GCD(12, 18) = 6

12/18 = 2/3

45/60

GCD(45, 60) = 15

45/60 = 3/4

100/250

GCD(100, 250) = 50

100/250 = 2/5

What is the GCD?

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF), is the largest positive integer that divides both numbers without a remainder. It can be found using the Euclidean algorithm or by comparing prime factorizations.

Why Simplify Fractions?

  • Makes fractions easier to understand and compare.
  • Simplifies further arithmetic operations like addition and multiplication.
  • Required in most math courses for final answers.
  • Helps identify equivalent fractions quickly.