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Greatest Common Divisor (GCD) of 142 and 112

The greatest common divisor (GCD) of 142 and 112 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 112?

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 ÷ 112 = 1 remainder 30
2 112 ÷ 30 = 3 remainder 22
3 30 ÷ 22 = 1 remainder 8
4 22 ÷ 8 = 2 remainder 6
5 8 ÷ 6 = 1 remainder 2
6 6 ÷ 2 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
158 and 1862
31 and 1281
101 and 111
195 and 1413
93 and 1821

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