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Greatest Common Divisor (GCD) of 47 and 67

The greatest common divisor (GCD) of 47 and 67 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 47 and 67?

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 ÷ 67 = 0 remainder 47
2 67 ÷ 47 = 1 remainder 20
3 47 ÷ 20 = 2 remainder 7
4 20 ÷ 7 = 2 remainder 6
5 7 ÷ 6 = 1 remainder 1
6 6 ÷ 1 = 6 remainder 0

Examples of GCD Calculations

NumbersGCD
65 and 2613
157 and 1111
138 and 393
200 and 1011
187 and 1011

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