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Greatest Common Divisor (GCD) of 172 and 123

The greatest common divisor (GCD) of 172 and 123 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 172 and 123?

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
1 172 ÷ 123 = 1 remainder 49
2 123 ÷ 49 = 2 remainder 25
3 49 ÷ 25 = 1 remainder 24
4 25 ÷ 24 = 1 remainder 1
5 24 ÷ 1 = 24 remainder 0

Examples of GCD Calculations

NumbersGCD
194 and 1802
199 and 1861
33 and 1083
167 and 1861
105 and 1911

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