Common Factors Calculator

Find common factors (common divisors) of a set of integers and identify the GCF.

Find common factors of two or more positive integers. Shows GCF and all factors with common ones highlighted.

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help_outlineHow to Useexpand_more

Finding Common Factors

This calculator finds all common factors (common divisors) shared by a set of positive integers. It also identifies the Greatest Common Factor (GCF), which is the largest number that divides evenly into all given numbers.

How to Find Common Factors:

  1. List factors: Find all factors (divisors) of each number
  2. Compare lists: Identify factors that appear in every list
  3. Common factors: Numbers that divide evenly into all given numbers
  4. Find GCF: The largest common factor is the GCF

What This Calculator Shows:

  • All common factors shared by the input numbers
  • The Greatest Common Factor (GCF)
  • Individual factor lists with common factors highlighted
infoWhat is Common Factors Calculator?expand_more

Common factors (also called common divisors) are numbers that divide evenly into two or more integers with no remainder. For example, the common factors of 12 and 18 are 1, 2, 3, and 6 because each of these divides both numbers evenly.

The factors of a number include all divisors of that number. For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12. You can divide 12 by any of these and get a whole number result.

Important: Every set of integers has at least one common factor: 1. The largest common factor is called the Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

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Definition of Common Factors:

A number F is a common factor of numbers A, B, C, ... if:

A mod F = 0 AND B mod F = 0 AND C mod F = 0 ...

(F divides evenly into all numbers)

Steps to Find Common Factors:

1. List all factors of each number

2. Find factors that appear in every list

3. These are the common factors

4. The largest one is the GCF

Greatest Common Factor:

GCF = largest number in the common factors list

Also known as GCD (Greatest Common Divisor) or HCF (Highest Common Factor)

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Example 1: Common Factors of 27, 54, and 81

Factors of 27: 1, 3, 9, 27

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Factors of 81: 1, 3, 9, 27, 81

Common factors: 1, 3, 9, 27 | GCF = 27

Example 2: Common Factors of 12 and 18

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6 | GCF = 6

Example 3: Common Factors of 24, 36, and 48

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors: 1, 2, 3, 4, 6, 12 | GCF = 12

Example 4: Coprime Numbers (7 and 11)

Factors of 7: 1, 7 (prime)

Factors of 11: 1, 11 (prime)

Common factor: 1 only | GCF = 1 (coprime)

quizFAQexpand_more
What is the difference between common factors and GCF?expand_more
Common factors are ALL numbers that divide evenly into every number in a set. The GCF (Greatest Common Factor) is specifically the LARGEST of these common factors. For example, 12 and 18 have common factors 1, 2, 3, and 6, but the GCF is just 6.
What does it mean if two numbers are coprime?expand_more
Two numbers are coprime (or relatively prime) when their only common factor is 1, meaning their GCF is 1. For example, 8 and 15 are coprime because they share no factors other than 1, even though neither is a prime number.
How are common factors useful?expand_more
Common factors are essential for simplifying fractions (divide both parts by the GCF), finding equivalent fractions, solving divisibility problems, and understanding number relationships. They're also used in scheduling and distribution problems.
Do all numbers have common factors?expand_more
Yes, every pair of positive integers has at least one common factor: 1. This is because 1 divides every integer evenly. Numbers with only 1 as their common factor are called coprime or relatively prime.
What is the relationship between common factors and GCF/GCD?expand_more
The GCF (Greatest Common Factor) or GCD (Greatest Common Divisor) is always the largest value in the list of common factors. All other common factors are divisors of the GCF itself.