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Greatest Common Divisor (GCD) of 78 and 190

The greatest common divisor (GCD) of 78 and 190 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 78 and 190?

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 78 ÷ 190 = 0 remainder 78
2 190 ÷ 78 = 2 remainder 34
3 78 ÷ 34 = 2 remainder 10
4 34 ÷ 10 = 3 remainder 4
5 10 ÷ 4 = 2 remainder 2
6 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
172 and 1511
63 and 1757
126 and 1222
169 and 1791
39 and 693

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