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Greatest Common Divisor (GCD) of 150 and 165

The greatest common divisor (GCD) of 150 and 165 is 15.

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 165?

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 ÷ 165 = 0 remainder 150
2 165 ÷ 150 = 1 remainder 15
3 150 ÷ 15 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
140 and 19010
140 and 15414
93 and 1641
82 and 102
199 and 1841

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