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Greatest Common Divisor (GCD) of 12 and 20

The greatest common divisor (GCD) of 12 and 20 is 4.

What is the Greatest Common Divisor (GCD)?

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.

How to Calculate the GCD of 12 and 20?

We use the Euclidean algorithm, which involves the following steps:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the smaller number and the smaller number with the remainder from the division.
  3. Repeat this process until the remainder is zero.
  4. The non-zero remainder just before zero is the GCD.

Step-by-Step Euclidean Algorithm

StepCalculation
1 12 ÷ 20 = 0 remainder 12
2 20 ÷ 12 = 1 remainder 8
3 12 ÷ 8 = 1 remainder 4
4 8 ÷ 4 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
82 and 722
92 and 891
164 and 262
134 and 1051
13 and 1831

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