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Greatest Common Divisor (GCD) of 116 and 105

The greatest common divisor (GCD) of 116 and 105 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 116 and 105?

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
1 116 ÷ 105 = 1 remainder 11
2 105 ÷ 11 = 9 remainder 6
3 11 ÷ 6 = 1 remainder 5
4 6 ÷ 5 = 1 remainder 1
5 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
173 and 251
131 and 771
194 and 1311
96 and 822
80 and 1616

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