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Greatest Common Divisor (GCD) of 42 and 121

The greatest common divisor (GCD) of 42 and 121 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 42 and 121?

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 42 ÷ 121 = 0 remainder 42
2 121 ÷ 42 = 2 remainder 37
3 42 ÷ 37 = 1 remainder 5
4 37 ÷ 5 = 7 remainder 2
5 5 ÷ 2 = 2 remainder 1
6 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
195 and 311
178 and 231
30 and 1893
80 and 1822
32 and 191

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