ggT- und kgV-Rechner
Der ggT von 16 und 24 ist 8. Dieser Rechner bestimmt den größten gemeinsamen Teiler und das kleinste gemeinsame Vielfache von zwei oder mehr natürlichen Zahlen, mit den Primfaktorzerlegungen.
Ergebnis
Gib Werte ein und tippe auf Berechnen, um das Ergebnis zu sehen.
Formel
For two numbers, the GCD and LCM multiply to the product of the numbers.
So benutzt du diesen Rechner
- Type the numbers, e.g. 12, 18, 30.
- Press Calculate to see the GCD, the LCM and each number’s prime factorisation.
Gelöste Beispiele
GCD and LCM of 12 and 18
12 = 2² × 3 and 18 = 2 × 3².
GCD takes the lowest powers: 2 × 3 = 6. LCM takes the highest: 2² × 3² = 36.
The GCF of 16 and 24
16 = 2⁴ and 24 = 2³ × 3. The greatest common factor takes the shared primes at their lowest power: 2³ = 8.
The LCM takes every prime at its highest power: 2⁴ × 3 = 48.
Check: 8 × 48 = 384 = 16 × 24.
The GCF of 16 and 36
16 = 2⁴ and 36 = 2² × 3². The only shared prime is 2, at power 2: GCF = 4.
LCM = 2⁴ × 3² = 144. Check: 4 × 144 = 576 = 16 × 36.
Häufige Fehler
- Mixing up GCF and LCM: the GCF is never bigger than the smallest number; the LCM is never smaller than the largest.
- Using the highest power for the GCF: for 16 = 2⁴ and 24 = 2³ × 3 the GCF uses 2³, not 2⁴.
- Stopping at a common factor that isn’t the greatest: 4 divides 16 and 24, but 8 is bigger.
Häufig gestellte Fragen
What is the GCF of 9 and 36?
9, because 9 divides 36 exactly (36 = 4 × 9). When one number divides the other, it is the GCF.
Are GCF, GCD and HCF the same?
Yes — greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF, the usual UK name) all mean the same number.
Is GCD the same as HCF or GCF?
Yes. Greatest common divisor, highest common factor and greatest common factor all mean the same thing.
Where is the LCM used?
Adding fractions uses the LCM of the denominators — the least common denominator.