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Greatest Common Divisor (GCD) of 102 and 117

The greatest common divisor (GCD) of 102 and 117 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 102 and 117?

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
1 102 ÷ 117 = 0 remainder 102
2 117 ÷ 102 = 1 remainder 15
3 102 ÷ 15 = 6 remainder 12
4 15 ÷ 12 = 1 remainder 3
5 12 ÷ 3 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
38 and 1351
69 and 1623
68 and 111
113 and 591
99 and 621

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