GCF calculator
Find the greatest common factor of 2 to 6 integers.
What this calculator covers
Use this calculator to find the largest factor shared by a set of integers before simplifying ratios or fractions.
The walkthrough focuses on Euclid's algorithm so the result is tied back to the remainder steps that produce it.
Frequently asked questions
- What is the greatest common factor?
- The greatest common factor (GCF) of a set of integers is the largest whole number that divides each of them evenly with no remainder. It is also called the greatest common divisor (GCD).
- How does Euclid's algorithm find the GCF?
- The algorithm replaces the larger number with the remainder of dividing the two numbers, then repeats until the remainder reaches zero. The last non-zero value in that chain is the GCF.
- When would I actually need the GCF?
- The most common use is simplifying a fraction to lowest terms — dividing both numerator and denominator by their GCF reduces the fraction without changing its value. It also helps when distributing items into equal groups.
- Can the GCF be larger than any of the input numbers?
- No. The GCF is always less than or equal to the smallest number in the set, because no divisor of a number can exceed the number itself.
Tool
Run the calculation
Result
RESULT · GCF
â„–152
Primary result
42
The greatest common factor of 84, 126, 210 is 42.
- Values used
- 84, 126, 210
- Greatest common factor
- 42
Step-by-step solution
- 1.List the integers 84, 126, 210.
- 2.Apply Euclid's algorithm pairwise until only the shared greatest divisor remains.
- 3.Read the final common factor as 42.
Walkthrough
Visual walkthrough
GCF work repeatedly strips away remainders until only the largest shared divisor survives.
01
Collect the integers
84, 126, 210
Only positive whole numbers are valid because GCF is defined on the integer inputs themselves.
02
Run Euclid's algorithm
gcd(a, b) = gcd(b, a mod b)
Each remainder step preserves the common divisors while shrinking the numbers.
03
Read the final shared factor
42
Once the remainder reaches zero, the last non-zero divisor is the greatest common factor.
42