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Greatest Common Divisor (GCD) of 94 and 77

The greatest common divisor (GCD) of 94 and 77 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 94 and 77?

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 94 ÷ 77 = 1 remainder 17
2 77 ÷ 17 = 4 remainder 9
3 17 ÷ 9 = 1 remainder 8
4 9 ÷ 8 = 1 remainder 1
5 8 ÷ 1 = 8 remainder 0

Examples of GCD Calculations

NumbersGCD
97 and 1711
171 and 1221
135 and 205
48 and 171
19 and 2001

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