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Greatest Common Divisor (GCD) of 141 and 190

The greatest common divisor (GCD) of 141 and 190 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 141 and 190?

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
1 141 ÷ 190 = 0 remainder 141
2 190 ÷ 141 = 1 remainder 49
3 141 ÷ 49 = 2 remainder 43
4 49 ÷ 43 = 1 remainder 6
5 43 ÷ 6 = 7 remainder 1
6 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
171 and 1899
114 and 7638
141 and 1931
200 and 631
151 and 1971

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