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Greatest Common Divisor (GCD) of 150 and 183

The greatest common divisor (GCD) of 150 and 183 is 3.

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 183?

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 ÷ 183 = 0 remainder 150
2 183 ÷ 150 = 1 remainder 33
3 150 ÷ 33 = 4 remainder 18
4 33 ÷ 18 = 1 remainder 15
5 18 ÷ 15 = 1 remainder 3
6 15 ÷ 3 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
30 and 711
98 and 802
45 and 1761
123 and 1113
69 and 1503

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