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Greatest Common Divisor (GCD) of 106 and 90

The greatest common divisor (GCD) of 106 and 90 is 2.

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 106 and 90?

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
1 106 ÷ 90 = 1 remainder 16
2 90 ÷ 16 = 5 remainder 10
3 16 ÷ 10 = 1 remainder 6
4 10 ÷ 6 = 1 remainder 4
5 6 ÷ 4 = 1 remainder 2
6 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
193 and 981
200 and 1964
142 and 811
90 and 1342
80 and 1484

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