Greatest Common Factor Calculator

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides two numbers without leaving a remainder.

Formula

The most common method to find the GCF of two numbers is the Euclidean Algorithm. For two numbers a and b where a > b:

  1. Divide a by b and get the remainder r.
  2. Replace a with b and b with r.
  3. Repeat the process until b becomes 0. The non-zero remainder then becomes the GCF.

Examples

Example 1: Find the GCF of 56 and 98

  1. 56 divided by 98 gives a quotient of 0 and a remainder of 56.
  2. Now, 98 divided by 56 gives a quotient of 1 and a remainder of 42.
  3. Then, 56 divided by 42 gives a quotient of 1 and a remainder of 14.
  4. Lastly, 42 divided by 14 gives a quotient of 3 and a remainder of 0. Hence, the GCF of 56 and 98 is 14.

Example 2: Find the GCF of 40 and 64

  1. 40 divided by 64 gives a quotient of 0 and a remainder of 40.
  2. Now, 64 divided by 40 gives a quotient of 1 and a remainder of 24.
  3. Then, 40 divided by 24 gives a quotient of 1 and a remainder of 16.
  4. Lastly, 24 divided by 16 gives a quotient of 1 and a remainder of 8. Hence, the GCF of 40 and 64 is 8.