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Greatest Common Divisor (GCD) of 176 and 69

The greatest common divisor (GCD) of 176 and 69 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 176 and 69?

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
1 176 ÷ 69 = 2 remainder 38
2 69 ÷ 38 = 1 remainder 31
3 38 ÷ 31 = 1 remainder 7
4 31 ÷ 7 = 4 remainder 3
5 7 ÷ 3 = 2 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
179 and 2001
24 and 1691
199 and 1851
113 and 251
194 and 1031

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