Greatest Common Factor (GCF) Calculator
Calculate the greatest common factor (GCF) / greatest common divisor (GCD) of two or more numbers. Get step‑by‑step prime factorization, factor lists, and visual charts.
Step 1: Enter Numbers
12
18
0
0
Positive integers only
Enter up to four positive integers. The calculator will find the greatest common factor (GCF) and show prime factors.
Step 2: Options
About GCF
The greatest common factor (GCF) of two or more integers is the largest positive integer that divides each number without a remainder.
GCF Calculation Results
Summary
Steps & Factors
Prime Charts
Greatest Common Factor (GCF)
6
of 12 and 18
Numbers entered
12, 18
LCM (if enabled)
36
Common factors
1, 2, 3, 6
Method used
Euclidean
Step‑by‑Step & Factor Lists
Using Euclidean algorithm for 12 and 18:
- 18 ÷ 12 = 1 remainder 6
- 12 ÷ 6 = 2 remainder 0
- GCF = 6
Factor lists:
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
Prime Factorization & Comparison
12 = 2² × 3¹
18 = 2¹ × 3²
GCF = 2¹ × 3¹ = 6
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