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Greatest Common Divisor (GCD) of 190 and 102

The greatest common divisor (GCD) of 190 and 102 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 190 and 102?

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
1 190 ÷ 102 = 1 remainder 88
2 102 ÷ 88 = 1 remainder 14
3 88 ÷ 14 = 6 remainder 4
4 14 ÷ 4 = 3 remainder 2
5 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
19 and 251
56 and 1288
109 and 741
169 and 1711
155 and 141

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