Common Factor Calculator
Find all common factors and the greatest common factor (GCF) of two numbers
Enter Two Numbers
Enter any positive or negative integer
Enter any positive or negative integer
Factor Analysis Results
Common Factors
Total: 6 common factors
Factors of 54
Total: 8 factors
Factors of 72
Total: 12 factors
Step-by-Step Solution
Example Calculations
Example 1: Numbers 54 and 72
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors: 1, 2, 3, 6, 9, 18
Greatest Common Factor (GCF): 18
Example 2: Numbers 12 and 24
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 4, 6, 12
Greatest Common Factor (GCF): 12
Factor Properties
Factor Definition
A number that divides evenly into another
Remainder is always zero
Common Factors
Factors shared by both numbers
Always includes 1
Greatest Common Factor
Largest common factor
Also called GCD
Key Concepts
Every integer has at least two factors: 1 and itself
Common factors are always divisors of both numbers
GCF is useful for simplifying fractions
For prime numbers, GCF with other numbers is usually 1
Factor pairs multiply to give the original number
Understanding Common Factors
What are Factors?
A factor of a number is any integer that divides evenly into that number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides into 12 exactly.
Common Factors
Common factors are numbers that are factors of two or more numbers. They represent the divisors that the numbers share. The greatest common factor (GCF) is the largest of these common factors.
Finding Factors
- •Start with 1 and the number itself
- •Test each integer from 2 to √n
- •If n ÷ i has no remainder, both i and n÷i are factors
Practical Applications
Fraction Simplification
Use GCF to reduce fractions to lowest terms
Example: 18/24 = (18÷6)/(24÷6) = 3/4
Problem Solving
Distribute items equally among groups
Example: Dividing pizza slices or inheritance
Number Theory
Foundation for understanding divisibility
Example: Prime factorization and modular arithmetic