Common Factor Calculator
Find common factors, GCF (Greatest Common Factor), and LCM of multiple numbers. See all factors and prime factorizations.
Factor Results
Greatest Common Factor
12
GCF of 2 numbers
Least Common Multiple
72
LCM
Enter Numbers
Enter at least 2 positive integers. Set to 0 to exclude.
Common Factors
1, 2, 3, 4, 6, 12
Greatest Common Factor (GCF)
12
Least Common Multiple (LCM)
72
All Factors
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
(8 factors)
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
(9 factors)
Prime Factorizations
How GCF is Calculated
Method 1: Common Factors
List factors of each number, find the largest one in all lists.
Factors of 24: {1, 2, 3, 4, 6, 8, 12, 24}
Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36}
Common: {1, 2, 3, 4, 6, 12}
GCF = 12
Method 2: Prime Factorization
Find common prime factors with lowest exponents, multiply together.
Method 3: Euclidean Algorithm
Repeatedly apply: GCF(a,b) = GCF(b, a mod b) until b = 0.
Factor Pairs
Factor pairs of 24:
Factor pairs of 36:
GCF × LCM Relationship
GCF(24, 36) × LCM(24, 36) = 24 × 36
12 × 72 = 24 × 36
864 = 864 ✓
Factor Results
Greatest Common Factor
12
GCF of 2 numbers
Least Common Multiple
72
LCM
?How Do You Find Common Factors?
Common factors are numbers that divide evenly into all given numbers. To find them: list all factors of each number, then identify the ones they share. For example, factors of 12 are {1,2,3,4,6,12}, factors of 18 are {1,2,3,6,9,18}. Common factors: {1,2,3,6}. The GCF is the largest: 6.
What is a Common Factor?
Common factors (or common divisors) are numbers that divide evenly into two or more integers without leaving a remainder. Finding common factors is fundamental to simplifying fractions, finding GCF and LCM, and understanding number relationships in arithmetic and algebra.
Key Facts About Common Factors
- Common factors divide evenly into all given numbers
- Every set of numbers has at least 1 as a common factor
- GCF (Greatest Common Factor) is the largest common factor
- Coprime numbers have only 1 as a common factor
- Common factors are found by comparing factor lists
- Useful for simplifying fractions (divide by GCF)
- Prime factorization method: find common primes
- The more numbers compared, generally fewer common factors
Quick Answer
Common factors are numbers that divide evenly into all given numbers. To find them: list all factors of each number, then identify the ones they share. For example, factors of 12 are {1,2,3,4,6,12}, factors of 18 are {1,2,3,6,9,18}. Common factors: {1,2,3,6}. The GCF is the largest: 6.
Frequently Asked Questions
A common factor is a number that divides two or more numbers evenly (without remainder). For example, 4 is a common factor of 12 and 20 because 12÷4=3 and 20÷4=5, both with no remainder. Common factors are also called common divisors.
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest number that divides two or more numbers evenly. For 12 and 18, the GCF is 6. The GCF is used to simplify fractions to lowest terms.
Method 1: List all factors of each number, then find which appear in both lists. Method 2: Use prime factorization - find common prime factors and multiply them. Method 3: Use the Euclidean algorithm for GCF, then factors of GCF are all common factors.
For any two numbers a and b: GCF(a,b) × LCM(a,b) = a × b. For example, GCF(12,18)=6 and LCM(12,18)=36, and 6×36=216=12×18. This relationship helps find one when you know the other.
Two numbers are coprime (or relatively prime) if their only common factor is 1, meaning GCF = 1. Examples: 8 and 15 are coprime (GCF=1), but 8 and 12 are not (GCF=4). Any two consecutive integers are always coprime.
Last updated: 2025-01-15
Factor Results
Greatest Common Factor
12
GCF of 2 numbers
Least Common Multiple
72
LCM