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Greatest Common Divisor (GCD) of 150 and 136

The greatest common divisor (GCD) of 150 and 136 is 2.

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 150 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
1 150 ÷ 136 = 1 remainder 14
2 136 ÷ 14 = 9 remainder 10
3 14 ÷ 10 = 1 remainder 4
4 10 ÷ 4 = 2 remainder 2
5 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
141 and 1773
21 and 4221
71 and 141
69 and 1923
148 and 131

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