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Greatest Common Divisor (GCD) of 122 and 88

The greatest common divisor (GCD) of 122 and 88 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 122 and 88?

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
1 122 ÷ 88 = 1 remainder 34
2 88 ÷ 34 = 2 remainder 20
3 34 ÷ 20 = 1 remainder 14
4 20 ÷ 14 = 1 remainder 6
5 14 ÷ 6 = 2 remainder 2
6 6 ÷ 2 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
119 and 601
151 and 231
74 and 571
106 and 1271
182 and 1091

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