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Greatest Common Divisor (GCD) of 200 and 65

The greatest common divisor (GCD) of 200 and 65 is 5.

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 200 and 65?

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
1 200 ÷ 65 = 3 remainder 5
2 65 ÷ 5 = 13 remainder 0

Examples of GCD Calculations

NumbersGCD
110 and 12111
35 and 1861
147 and 1791
77 and 14311
12 and 1811

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