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Greatest Common Divisor (GCD) of 77 and 165

The greatest common divisor (GCD) of 77 and 165 is 11.

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 77 and 165?

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 77 ÷ 165 = 0 remainder 77
2 165 ÷ 77 = 2 remainder 11
3 77 ÷ 11 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
97 and 1551
93 and 1181
32 and 1451
23 and 1871
119 and 18717

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