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Greatest Common Divisor (GCD) of 142 and 176

The greatest common divisor (GCD) of 142 and 176 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 176?

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 ÷ 176 = 0 remainder 142
2 176 ÷ 142 = 1 remainder 34
3 142 ÷ 34 = 4 remainder 6
4 34 ÷ 6 = 5 remainder 4
5 6 ÷ 4 = 1 remainder 2
6 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
109 and 181
41 and 721
106 and 1782
64 and 1491
81 and 1931

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