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Greatest Common Divisor (GCD) of 36 and 174

The greatest common divisor (GCD) of 36 and 174 is 6.

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 36 and 174?

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 36 ÷ 174 = 0 remainder 36
2 174 ÷ 36 = 4 remainder 30
3 36 ÷ 30 = 1 remainder 6
4 30 ÷ 6 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
14 and 1071
195 and 1781
145 and 1491
76 and 171
71 and 161

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