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Greatest Common Divisor (GCD) of 89 and 165

The greatest common divisor (GCD) of 89 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 89 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 89 ÷ 165 = 0 remainder 89
2 165 ÷ 89 = 1 remainder 76
3 89 ÷ 76 = 1 remainder 13
4 76 ÷ 13 = 5 remainder 11
5 13 ÷ 11 = 1 remainder 2
6 11 ÷ 2 = 5 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
30 and 1331
40 and 1431
195 and 641
185 and 271
38 and 11438

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