Common Factor Calculator
Enter two integers to list every factor of each, highlight their shared factors, and compute the greatest common divisor (GCD) via the Euclidean algorithm — plus the least common multiple (LCM) for free.
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GCD(12, 18)
6
LCM = 36 · 4 common factors
- Greatest common divisor
- 6
- Least common multiple
- 36
- Factors of 12
- 1, 2, 3, 4, 6, 12
- Factors of 18
- 1, 2, 3, 6, 9, 18
- Common factors
- 1, 2, 3, 6
- Coprime (GCD = 1)?
- No
Euclidean algorithm for GCD
- 112 = 0 × 18 + 12
- 218 = 1 × 12 + 6
- 312 = 2 × 6 + 0
- 4Remainder reached 0 → GCD(12, 18) = 6
Factor lists
Most useful next
Formula
Euclid: a = q·b + r, repeat with (a,b) → (b,r) until r = 0 · GCD × LCM = a × b
Pro tips
- • GCD is the largest number that divides both inputs — useful for simplifying fractions.
- • LCM = a × b / GCD, handy for adding fractions with different denominators.
- • Two numbers with GCD 1 are called coprime.
FAQ
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