Greatest Common Factor Calculator
Find the GCF and LCM of two or more numbers with prime factorisation and step-by-step Euclidean algorithm working
GCF (Greatest Common Factor)
12
LCM (Least Common Multiple)
72
Prime Factorizations
Euclidean Algorithm Steps
GCF(24, 36) calculated by repeatedly finding remainders until remainder is 0. Result = 12
Finding the GCF of Two or More Numbers
GCF (Greatest Common Factor, or GCD) is the largest number that divides each of the given numbers without remainder. For 12 and 18: divisors of 12 are 1, 2, 3, 4, 6, 12; divisors of 18 are 1, 2, 3, 6, 9, 18. Common: 1, 2, 3, 6. Greatest: 6. So GCF(12, 18) = 6.
Used to simplify fractions: 12/18 reduces to 2/3 by dividing both top and bottom by GCF 6. Used in algebra to factor expressions, in number theory, and in algorithms (Euclid's algorithm efficiently finds GCF). Practical applications: dividing materials evenly, scaling recipes proportionally, simplifying gear ratios.
GCF Examples
| Numbers | GCF |
|---|---|
| 8, 12 | 4 |
| 12, 18 | 6 |
| 15, 25 | 5 |
| 24, 36 | 12 |
| 30, 45 | 15 |
| 48, 60 | 12 |
| 100, 75 | 25 |
| 7, 11 (coprime) | 1 |
Frequently Asked Questions
What's Euclid's algorithm?
Efficient method for finding GCF without listing all divisors. Repeatedly divide larger by smaller, take remainder, replace larger with smaller and smaller with remainder. Stop when remainder is 0; last divisor is GCF. Example: GCF(48, 36): 48÷36 = 1 rem 12. 36÷12 = 3 rem 0. GCF = 12.
What if the GCF is 1?
Numbers are 'coprime' or 'relatively prime'. Their only common divisor is 1. Examples: any two distinct primes (like 7 and 11), or any number paired with 1. Coprime numbers can't be simplified as fractions further.