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Greatest Common Divisor (GCD) of 83 and 165

The greatest common divisor (GCD) of 83 and 165 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 83 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 83 ÷ 165 = 0 remainder 83
2 165 ÷ 83 = 1 remainder 82
3 83 ÷ 82 = 1 remainder 1
4 82 ÷ 1 = 82 remainder 0

Examples of GCD Calculations

NumbersGCD
49 and 941
83 and 1471
198 and 1851
19 and 591
60 and 933

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