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Greatest Common Divisor (GCD) of 196 and 34

The greatest common divisor (GCD) of 196 and 34 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 196 and 34?

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
1 196 ÷ 34 = 5 remainder 26
2 34 ÷ 26 = 1 remainder 8
3 26 ÷ 8 = 3 remainder 2
4 8 ÷ 2 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
39 and 1781
124 and 951
164 and 982
88 and 611
134 and 482

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