Common Factors Calculator: Find Factors and GCF
Enter two or more whole numbers to instantly find their common factors and greatest common factor
| Number | Factors |
|---|
Common factors calculator finds shared divisors fast
Common factors calculator tools let you find every factor of two or more numbers and identify which factors they share, including the greatest common factor. This is useful for simplifying fractions, splitting groups evenly, and solving number theory problems in math class.
How the common factors calculator works
The common factors calculator works by listing every factor of each number you enter, then comparing the lists to find the values that appear in all of them. The largest shared value becomes the greatest common factor, often abbreviated as GCF.
Common factors explain how numbers relate to each other
Common factors explain which whole numbers can divide evenly into a group of numbers without leaving a remainder. A factor of a number is any whole number that divides it exactly, and a common factor is a factor shared by all numbers in the set.
Example with three numbers
Consider the numbers 27, 54 and 81. The factors of 27 are 1, 3, 9 and 27. The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. The factors of 81 are 1, 3, 9, 27 and 81. The numbers shared by all three lists are 1, 3, 9 and 27, so the greatest common factor of 27, 54 and 81 is 27.
Finding the GCF step by step
- List all factors of each number by dividing it by every whole number up to itself
- Compare the factor lists and identify the values that appear in every list
- Select the largest value from the shared list as the greatest common factor
Reference table shows common GCF examples
Reference table data below shows the greatest common factor for several common pairs and groups of numbers.
| Numbers | Common Factors | GCF |
|---|---|---|
| 12, 18 | 1, 2, 3, 6 | 6 |
| 24, 36 | 1, 2, 3, 4, 6, 12 | 12 |
| 16, 24, 64, 136 | 1, 2, 4, 8 | 8 |
| 45, 60 | 1, 3, 5, 15 | 15 |
| 100, 75 | 1, 5, 25 | 25 |
Real world common factors apply to grouping and simplifying
Real world common factors come up whenever you need to split items into equal groups or reduce a fraction to its simplest form. Knowing the GCF helps you divide a set of objects evenly or simplify ratios in cooking, construction, and finance.
Common uses for the GCF
- Simplifying fractions to their lowest terms
- Dividing a collection of items into equal sized groups
- Reducing ratios in recipes or mixtures
- Solving number theory and divisibility problems in school
Frequently asked questions about common factors
Common factors are numbers that divide evenly into two or more given numbers without leaving a remainder. They are found by listing the factors of each number and identifying which factors appear in every list.
The greatest common factor, often called the GCF, is the largest number that divides evenly into all of the given numbers. It is the biggest value among the shared common factors.
To find the factors of a number, divide it by every whole number from 1 up to the number itself and keep the divisors that produce a whole number result with no remainder. These divisors are the complete list of factors for that number.
The greatest common factor of 16, 24, 64 and 136 is 8. The full list of common factors shared by all four numbers is 1, 2, 4 and 8.
This calculator accepts two or more positive whole numbers separated by commas. There is no fixed limit, so you can enter as many numbers as needed to find their shared factors.
The greatest common factor is useful for simplifying fractions, reducing ratios, and solving problems that involve dividing groups of items into equal sized sets. Dividing the numerator and denominator of a fraction by their GCF produces the simplest form of that fraction.