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Greatest Common Divisor (GCD) of 120 and 136

The greatest common divisor (GCD) of 120 and 136 is 8.

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 120 and 136?

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
1 120 ÷ 136 = 0 remainder 120
2 136 ÷ 120 = 1 remainder 16
3 120 ÷ 16 = 7 remainder 8
4 16 ÷ 8 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
79 and 961
123 and 351
154 and 1462
60 and 191
80 and 631

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