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Common factor calculator

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This common factor calculator determines the common factors, the greatest common factor, and provides factorizations for the given numbers.

Related calculators:

Factor calculatorGreatest common factor

What is a factor?

In mathematics, a factor is a number that divides another number evenly, meaning that when you divide the larger number by the factor, there is no remainder. For example, in the case of the number 12, its factors are 1, 2, 3, 4, 6, and 12 because:

  •  12 \div 1 = 12 
  •  12 \div 2 = 6 
  •  12 \div 3 = 4 
  •  12 \div 4 = 3 
  •  12 \div 6 = 2 
  •  12 \div 12 = 1 

How to calculate factors

  1. Identify the number: Start with the number for which you want to find factors.
  2. Check divisibility: Check numbers starting from 1 up to the number itself to see if they divide the number evenly.
    • For each number  n, check if  \text{number} \mod n = 0 . If true, n is a factor.
  3. List all factors: Continue this process until you’ve checked all numbers up to the given number.

Example: Finding factors of 18

  1. Start with the number 18.
  2. Check numbers from 1 to 18:
    • 1 (yes), 2 (yes), 3 (yes), 4 (no), 5 (no), 6 (yes), 7 (no), 8 (no), 9 (yes), 10 (no), 11 (no), 12 (no), 13 (no), 14 (no), 15 (no), 16 (no), 17 (no), 18 (yes).
  3. Factors of 18 are: 1, 2, 3, 6, 9, and 18.

What is a common factor?

A common factor is a number that divides two or more numbers without leaving a remainder. In other words, it’s a factor that is shared by each of the numbers in a given set. For example, in the numbers 12 and 18, the common factors are 1, 2, 3, and 6, since all of these numbers can divide both 12 and 18 evenly. The greatest common factor (GCF) is the largest of these common factors.

How to calculate common factors

To find the common factors of a given set of numbers, follow these steps:

  1. List the factors: Start by listing all the factors for each number. A factor is a whole number that can be divided evenly into another number.
  2. Identify the common factors: Compare the lists of factors to identify which factors appear in all lists. These are your common factors.
  3. Greatest common factor (GFC): To find the greatest common factor, identify the largest number in the list of common factors.

Example: Finding common factors of 12 and 18

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

Common Factors: 1, 2, 3, 6
Greatest Common Factor (GFC): 6

Alternative method:

You can also use the prime factorization method:

  1. Find Prime factorizations: Break down each number into its prime factors.
  2. Identify common prime factors: Find the common prime factors among the numbers.
  3. Multiply the lowest powers: Multiply the common prime factors using their lowest powers to get the GCF.