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Greatest Common Divisor (GCD) of 60 and 199

The greatest common divisor (GCD) of 60 and 199 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 60 and 199?

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 60 ÷ 199 = 0 remainder 60
2 199 ÷ 60 = 3 remainder 19
3 60 ÷ 19 = 3 remainder 3
4 19 ÷ 3 = 6 remainder 1
5 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
172 and 1422
173 and 1761
106 and 1802
196 and 1631
184 and 382

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