Fraction, Mixed Number, GCF, LCM & Prime Factorization Calculator

Perform exact rational fraction arithmetic and compute GCF, LCM, long division remainder, and prime factors.

Exact Simplified Fraction & Mixed Number
19/12 (1.583333)
Mixed: 1 7/12 • LCD of denominators (4, 6) = 12
Quotient & Remainder Q = 1, R = 7
GCF & LCM of (4, 6) GCF = 2, LCM = 12
Prime Factors of 24 2 × 2 × 2 × 3
Decimal Equivalent 1.583333
Inputs
Top integer of first fraction (a/b).
Bottom integer of first fraction (also used for GCF/LCM).
Operation applied between (a/b) and (c/d).
Top integer of second fraction (c/d).
Bottom integer of second fraction (also used for GCF/LCM).
Results & Graph
Exact Simplified Fraction & Mixed Number
19/12 (1.583333)
Mixed: 1 7/12 • LCD of denominators (4, 6) = 12
Quotient & Remainder
Q = 1, R = 7
GCF & LCM of (4, 6)
GCF = 2, LCM = 12
Prime Factors of 24
2 × 2 × 2 × 3
Decimal Equivalent
1.583333

Decimal Magnitude Comparison

First Fraction vs. Second Fraction vs. Result
Graph 1 • Partitioned Fraction Grid Bars Shaded numerator cells out of denominator partitions
Fraction 1 (3/4)0.7500 Fraction 2 (5/6)0.8333 Result (1.583)1.5833
Graph 2 • Exact Coordinate Placement on the Real Number Line Plots Fraction 1, Fraction 2, and Combined Result
3/4 (0.75) 5/6 (0.83) Result = 1.5833 0 1.0 2
Graph 3 • Fraction Magnitudes & Common Denominator Scale Reduced via Euclidean Greatest Common Divisor (GCD)
First (3/4) 0.75 Second (5/6) 0.833 Result (19/12) 1.583
Summary: Simplified fraction is 19/12 (1.5833), GCF is 2, and LCM is 12.
Summary: Evaluating (3/4) and (5/6) yields 38/24, which reduces via GCF (2) to 19/12 (decimal 1.583333). For the denominators 4 and 6, the Greatest Common Factor is 2 and Least Common Multiple (LCD) is 12.

Formula & Mathematical Methodology: Rational Arithmetic & Euclidean GCD / LCM Identities

ab ± cd = ad ± bcbd,   lcm(b, d) = |b · d|gcd(b, d)
a/b ± c/d = (ad ± bc) / bd; gcd(x, y) via Euclid; lcm(b, d) = |b × d| / gcd(b, d)
  • gcd(x, y): Greatest Common Divisor (Factor) of integers x and y
  • lcm(b, d): Least Common Multiple (Least Common Denominator)

Rounding: Exact integer rational reduction; decimal readout rounded to 6 places.

Worked Example: Add 3/4 + 5/6 and Find GCF & LCM of 4 and 6

Compute 3/4 + 5/6 in simplest improper and mixed-number form.

  1. GCF(4, 6) = 2; Least Common Denominator LCM(4, 6) = (4 × 6) ÷ 2 = 12.
  2. 3/4 + 5/6 = 9/12 + 10/12 = 19/12.
  3. Long division: 19 ÷ 12 = Quotient 1, Remainder 7 → Mixed number 1 7/12 (1.583333).
Result: 19/12 = 1 7/12 (1.583333); GCF(4,6) = 2, LCM(4,6) = 12.

Frequently Asked Questions

How are GCF and LCM mathematically connected?

For any two positive integers a and b, the product of their Greatest Common Factor and Least Common Multiple equals the product of the numbers themselves: GCF(a, b) × LCM(a, b) = a × b.

Mathematics & Statistics • Rational Arithmetic & Number Theory Guide

How to Use the Fraction, Mixed Number, GCF, LCM & Prime Factorization Calculator: Practical Guide & Visual Analysis

Solve fraction addition, subtraction, multiplication, and division with automatic Euclidean GCD reduction, mixed-number conversion, Least Common Denominator (LCD), and prime factor trees. Whether you are researching fraction calculator, greatest common factor calculator, least common multiple calculator, prime factorization calculator, long division calculator, this interactive tool helps you add, subtract, multiply, or divide fractions into simplest form and mixed numbers, and compute GCF, LCM, quotient/remainder, and prime factorizations.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust First Fraction Numerator (a), First Fraction Denominator (b), Arithmetic Operation, Second Fraction Numerator (c), the calculator immediately computes Simplified Irreducible Fraction, Mixed Number & Long Division (Quotient / Remainder), GCF & LCM of Denominators, Prime Factorization and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Global)

In our benchmark scenario (Add 3/4 + 5/6 and Find GCF & LCM of 4 and 6), 19/12 = 1 7/12 (1.583333); GCF(4,6) = 2, LCM(4,6) = 12. Keep in mind that inputs are truncated to integers for exact rational and prime factorization arithmetic. For related calculations in Mathematics & Statistics, explore Scientific Calculator, Percentage Calculator, Quadratic Formula, Slope, Distance & Half-Life Calculator.