Math Tools
Greatest Common Factor Calculator
Find the greatest common factor and all common factors of whole numbers.
Greatest Common Factor Calculator
Find the greatest common factor shared by two or more whole numbers.
Example: 12, 18, 24
Results
Greatest common factor
6
Common factors
1, 2, 3, 6
Numbers used
12, 18, 24
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What this calculator does
This calculator finds the greatest common factor shared by two or more whole numbers and also lists all common factors. It is useful when you want a fast answer for GCF problems, factor practice, fraction simplification, or equal grouping questions.
What is the greatest common factor?
The greatest common factor, also called GCF, is the largest whole number that divides two or more whole numbers evenly. If a number can divide every value in the set without leaving a remainder, it is a common factor. The greatest one among those is the GCF.
For example, the common factors of 12 and 18 are 1, 2, 3, and 6, so the greatest common factor is 6. This idea is useful in arithmetic, fractions, algebra, factorization, and many classroom math problems.
How to find the greatest common factor
To find the greatest common factor, first list the factors of each whole number. Then identify which factors are shared by all the numbers. The largest shared factor is the GCF.
Another common method is prime factorization. Break each number into prime factors, then multiply the prime factors they all share. Both methods lead to the same GCF, but a calculator is much faster when several numbers are involved.
Greatest common factor examples and common factor table
| Numbers | GCF | Common factors |
|---|---|---|
| 12, 18 | 6 | 1, 2, 3, 6 |
| 12, 18, 24 | 6 | 1, 2, 3, 6 |
| 20, 30, 50 | 10 | 1, 2, 5, 10 |
| 16, 24, 40 | 8 | 1, 2, 4, 8 |
Why the greatest common factor is useful
The greatest common factor is especially useful when simplifying fractions. If the numerator and denominator share a common factor, dividing both by the GCF reduces the fraction to its simplest form.
GCF is also used in algebra, grouping expressions, solving word problems, and dividing quantities into equal groups. It helps you find the largest possible equal grouping without leftovers.
GCF vs LCM: what is the difference?
GCF means greatest common factor, while LCM means least common multiple. The GCF is the largest factor that divides all the numbers, while the LCM is the smallest multiple shared by all the numbers.
If you are simplifying fractions or factoring expressions, you usually need the GCF. If you are matching cycles, denominators, or repeated intervals, you usually need the LCM instead.
Step-by-step example of finding the GCF
Take the numbers 12, 18, and 24. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The shared factors are 1, 2, 3, and 6. The greatest of these is 6, so the greatest common factor of 12, 18, and 24 is 6.
Where a greatest common factor calculator is helpful
A greatest common factor calculator is useful for students, teachers, parents, and anyone reviewing arithmetic or algebra. It saves time when checking homework, simplifying fractions, or practicing factor problems.
It is also useful when working with equal grouping problems, ratios, and number patterns because it quickly shows both the GCF and all shared factors for the numbers you enter.
Greatest common factor calculator FAQ and common questions
What is the greatest common factor?
The greatest common factor is the largest whole number that divides two or more whole numbers evenly.
How do you find the GCF of two numbers?
You can list the factors of both numbers, find the shared factors, and choose the largest one. A calculator does this automatically for you.
What is the GCF of 12, 18, and 24?
The greatest common factor of 12, 18, and 24 is 6.
Is greatest common factor the same as highest common factor?
Yes. Greatest common factor and highest common factor mean the same thing.
What is the difference between GCF and LCM?
GCF is the largest shared factor, while LCM is the smallest shared multiple.
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