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Greatest Common Divisor (GCD) of 31 and 196

The greatest common divisor (GCD) of 31 and 196 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 31 and 196?

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 31 ÷ 196 = 0 remainder 31
2 196 ÷ 31 = 6 remainder 10
3 31 ÷ 10 = 3 remainder 1
4 10 ÷ 1 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
197 and 1041
171 and 341
108 and 1284
45 and 1605
135 and 6015

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