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Greatest Common Divisor (GCD) of 142 and 198

The greatest common divisor (GCD) of 142 and 198 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 142 and 198?

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
1 142 ÷ 198 = 0 remainder 142
2 198 ÷ 142 = 1 remainder 56
3 142 ÷ 56 = 2 remainder 30
4 56 ÷ 30 = 1 remainder 26
5 30 ÷ 26 = 1 remainder 4
6 26 ÷ 4 = 6 remainder 2
7 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
132 and 573
97 and 1451
40 and 1531
58 and 891
179 and 121

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