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Greatest Common Divisor (GCD) of 93 and 109

The greatest common divisor (GCD) of 93 and 109 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 93 and 109?

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 93 ÷ 109 = 0 remainder 93
2 109 ÷ 93 = 1 remainder 16
3 93 ÷ 16 = 5 remainder 13
4 16 ÷ 13 = 1 remainder 3
5 13 ÷ 3 = 4 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
199 and 1211
75 and 1155
138 and 1522
119 and 1141
58 and 911

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