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Greatest Common Divisor (GCD) of 67 and 74

The greatest common divisor (GCD) of 67 and 74 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 67 and 74?

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 67 ÷ 74 = 0 remainder 67
2 74 ÷ 67 = 1 remainder 7
3 67 ÷ 7 = 9 remainder 4
4 7 ÷ 4 = 1 remainder 3
5 4 ÷ 3 = 1 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
173 and 1601
175 and 1267
124 and 124
61 and 2001
139 and 1021

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