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Greatest Common Divisor (GCD) of 28 and 133

The greatest common divisor (GCD) of 28 and 133 is 7.

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 28 and 133?

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 28 ÷ 133 = 0 remainder 28
2 133 ÷ 28 = 4 remainder 21
3 28 ÷ 21 = 1 remainder 7
4 21 ÷ 7 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
159 and 701
29 and 1601
20 and 271
43 and 401
106 and 1762

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