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Greatest Common Divisor (GCD) of 180 and 77

The greatest common divisor (GCD) of 180 and 77 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 180 and 77?

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
1 180 ÷ 77 = 2 remainder 26
2 77 ÷ 26 = 2 remainder 25
3 26 ÷ 25 = 1 remainder 1
4 25 ÷ 1 = 25 remainder 0

Examples of GCD Calculations

NumbersGCD
115 and 1755
122 and 1182
90 and 819
32 and 591
167 and 621

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