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Greatest Common Divisor (GCD) of 142 and 163

The greatest common divisor (GCD) of 142 and 163 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 142 and 163?

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 ÷ 163 = 0 remainder 142
2 163 ÷ 142 = 1 remainder 21
3 142 ÷ 21 = 6 remainder 16
4 21 ÷ 16 = 1 remainder 5
5 16 ÷ 5 = 3 remainder 1
6 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
172 and 971
143 and 641
61 and 291
133 and 931
139 and 461

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