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Greatest Common Divisor (GCD) of 117 and 177

The greatest common divisor (GCD) of 117 and 177 is 3.

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 117 and 177?

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
1 117 ÷ 177 = 0 remainder 117
2 177 ÷ 117 = 1 remainder 60
3 117 ÷ 60 = 1 remainder 57
4 60 ÷ 57 = 1 remainder 3
5 57 ÷ 3 = 19 remainder 0

Examples of GCD Calculations

NumbersGCD
23 and 911
178 and 1742
150 and 111
133 and 1451
176 and 631

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