Factor Fractions Calculator

Factor numerators and denominators into primes with clarity. See common factors, reductions, and mixed-number results. Export results instantly and compare fraction structure through charts.

Calculator Input

Use a negative whole part for negative mixed numbers.
Reset

Example Data Table

Input Improper Fraction GCD Simplified Fraction Mixed Form Decimal
18/24 18/24 6 3/4 3/4 0.75
1 14/28 42/28 14 3/2 1 1/2 1.5
-2 9/15 -39/15 3 -13/5 -2 3/5 -2.6
45/120 45/120 15 3/8 3/8 0.375

Formula Used

Improper Numerator = (|Whole Part| × Denominator) + |Numerator|

Apply the sign from the whole part when a mixed number is entered. If no whole part is used, the typed numerator becomes the working numerator.

GCD = greatest common divisor of numerator and denominator

The greatest common divisor is the largest positive integer dividing both values exactly. It gives the full cancellation amount for simplification.

Simplified Fraction = Numerator ÷ GCD over Denominator ÷ GCD

Once both parts are divided by the same greatest common divisor, the result is the fraction in lowest terms.

Decimal Value = Simplified Numerator ÷ Simplified Denominator

The decimal is rounded to the number of places selected in the form.

Percentage = Decimal Value × 100

This converts the simplified fraction into a percentage while preserving the selected precision.

Prime Factorization = product of prime powers

Each number is written as primes raised to exponents. Common primes reveal the exact shared factors that can be cancelled.

How to Use This Calculator

  1. Enter a whole part only when your value is a mixed number, such as 2 3/5.
  2. Type the numerator and denominator of the fraction you want to factor.
  3. Choose decimal places for the decimal and percentage outputs.
  4. Set the factor list limit to control how many listed factors appear.
  5. Choose whether factor lists should be displayed.
  6. Press Factor Fraction to place the result below the header and above the form.
  7. Review the simplified fraction, mixed form, prime factors, factor lists, and graph.
  8. Use the CSV and PDF buttons to export your result summary.

FAQs

1. What does this calculator actually factor?

It factors the working numerator and denominator into prime factors, finds their greatest common divisor, and reduces the fraction to lowest terms.

2. Can I enter mixed numbers?

Yes. Enter the whole part in the first box, then enter the fractional numerator and denominator. The calculator converts the value to an improper fraction automatically.

3. How are negative fractions handled?

Use a negative whole part for negative mixed numbers, or a negative numerator when no whole part is used. Keep the denominator positive for clean interpretation.

4. Why is prime factorization not shown for zero?

Zero does not have a standard prime factorization because every non-zero integer divides zero. The calculator still simplifies the fraction correctly.

5. What does the graph represent?

The Plotly graph compares prime exponents in the numerator, denominator, and shared common factors. This makes cancellation patterns easy to see visually.

6. What is the factor list limit for?

Some integers have many factors. The factor list limit controls how many listed factors appear, keeping results readable while still showing useful structure.

7. Does the calculator also show decimal and percent forms?

Yes. After simplification, it converts the result into decimal and percentage forms using the number of decimal places you selected.

8. Can I export my results?

Yes. Use the CSV button for spreadsheet-friendly data and the PDF button for a clean document summary of the fraction analysis.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.