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Greatest Common Divisor (GCD) of 200 and 165

The greatest common divisor (GCD) of 200 and 165 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 165?

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 ÷ 165 = 1 remainder 35
2 165 ÷ 35 = 4 remainder 25
3 35 ÷ 25 = 1 remainder 10
4 25 ÷ 10 = 2 remainder 5
5 10 ÷ 5 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
90 and 111
127 and 731
47 and 501
74 and 611
61 and 1781

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