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Greatest Common Divisor (GCD) of 47 and 141

The greatest common divisor (GCD) of 47 and 141 is 47.

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 47 and 141?

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 47 ÷ 141 = 0 remainder 47
2 141 ÷ 47 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
194 and 911
74 and 791
142 and 851
18 and 471
102 and 1542

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