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Greatest Common Divisor (GCD) of 155 and 116

The greatest common divisor (GCD) of 155 and 116 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 155 and 116?

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
1 155 ÷ 116 = 1 remainder 39
2 116 ÷ 39 = 2 remainder 38
3 39 ÷ 38 = 1 remainder 1
4 38 ÷ 1 = 38 remainder 0

Examples of GCD Calculations

NumbersGCD
91 and 1771
199 and 1311
61 and 1071
33 and 291
121 and 1171

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