This GCF calculator finds the greatest common factor (also called GCD or HCF) of two or more numbers — plus their least common multiple (LCM) — and shows each number’s factors so you can see why the answer is what it is.
What Is the Greatest Common Factor?
The GCF of a set of numbers is the largest number that divides into all of them evenly. It is the key to simplifying fractions (divide top and bottom by the GCF), factoring expressions in algebra, and splitting things into the largest possible equal groups. GCF, GCD (greatest common divisor) and HCF (highest common factor) are three names for the same thing. This calculator is part of our Math Calculators collection.
Worked Example (Verified)
GCF of 48 and 180:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
- Common factors: 1, 2, 3, 4, 6, 12 → the greatest is 12
- And the LCM of 48 and 180 is 720 — note the identity: GCF × LCM = 48 × 180 = 8,640 = 12 × 720 ✔
How to Find the GCF (Prime Factorization Method)
- Break each number into primes: 48 = 2⁴ × 3; 180 = 2² × 3² × 5.
- Take the lowest power of each shared prime: 2² × 3¹ = 12.
- For the LCM, take the highest power of every prime involved: 2⁴ × 3² × 5 = 720.
- For big numbers, Euclid’s algorithm (repeated remainders, used by this calculator) is much faster than listing factors.
The most common everyday use: reducing fractions — 48/180 simplifies by 12 to 4/15. Do that step automatically with our Fraction Calculator, and count arrangements of the numbers with the Factorial Calculator.
Related Tools
- Fraction Calculator — simplify and compute fractions
- Factorial Calculator
- Math Calculators — the full collection
Frequently Asked Questions
What is the GCF of 48 and 180?
12. The common factors are 1, 2, 3, 4, 6 and 12; twelve is the greatest.
Are GCF, GCD and HCF the same?
Yes — greatest common factor, greatest common divisor and highest common factor are identical; different textbooks and countries prefer different names.
What is the GCF if the numbers share no factors?
1 — the numbers are called coprime or relatively prime (like 8 and 15).
How are GCF and LCM related?
For two numbers, GCF × LCM = the product of the numbers. Find one and you can always get the other.
Can the GCF be bigger than the smaller number?
No — a factor of a number cannot exceed the number itself, so the GCF is at most the smallest number in the set (and equals it when the smallest divides all the others).
Is this GCF calculator free?
Yes — free, instant, no sign-up.