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Greatest Common Divisor (GCD) of 97 and 77

The greatest common divisor (GCD) of 97 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 97 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 97 ÷ 77 = 1 remainder 20
2 77 ÷ 20 = 3 remainder 17
3 20 ÷ 17 = 1 remainder 3
4 17 ÷ 3 = 5 remainder 2
5 3 ÷ 2 = 1 remainder 1
6 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
122 and 1371
80 and 1655
152 and 1891
71 and 1841
179 and 1171

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