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Greatest Common Divisor (GCD) of 133 and 200

The greatest common divisor (GCD) of 133 and 200 is 1.

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 133 and 200?

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
1 133 ÷ 200 = 0 remainder 133
2 200 ÷ 133 = 1 remainder 67
3 133 ÷ 67 = 1 remainder 66
4 67 ÷ 66 = 1 remainder 1
5 66 ÷ 1 = 66 remainder 0

Examples of GCD Calculations

NumbersGCD
187 and 281
196 and 1524
61 and 431
196 and 684
102 and 282

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