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Greatest Common Divisor (GCD) of 137 and 166

The greatest common divisor (GCD) of 137 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 137 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
1 137 ÷ 166 = 0 remainder 137
2 166 ÷ 137 = 1 remainder 29
3 137 ÷ 29 = 4 remainder 21
4 29 ÷ 21 = 1 remainder 8
5 21 ÷ 8 = 2 remainder 5
6 8 ÷ 5 = 1 remainder 3
7 5 ÷ 3 = 1 remainder 2
8 3 ÷ 2 = 1 remainder 1
9 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
165 and 1593
132 and 1462
59 and 241
122 and 1762
173 and 221

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