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Greatest Common Divisor (GCD) of 89 and 166

The greatest common divisor (GCD) of 89 and 166 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 166?

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 ÷ 166 = 0 remainder 89
2 166 ÷ 89 = 1 remainder 77
3 89 ÷ 77 = 1 remainder 12
4 77 ÷ 12 = 6 remainder 5
5 12 ÷ 5 = 2 remainder 2
6 5 ÷ 2 = 2 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
24 and 311
56 and 1484
35 and 521
53 and 1441
27 and 8127

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