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Greatest Common Divisor (GCD) of 158 and 121

The greatest common divisor (GCD) of 158 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 158 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
1 158 ÷ 121 = 1 remainder 37
2 121 ÷ 37 = 3 remainder 10
3 37 ÷ 10 = 3 remainder 7
4 10 ÷ 7 = 1 remainder 3
5 7 ÷ 3 = 2 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
187 and 251
48 and 7224
199 and 1471
115 and 1861
28 and 1511

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