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Greatest Common Divisor (GCD) of 150 and 104

The greatest common divisor (GCD) of 150 and 104 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 104?

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 ÷ 104 = 1 remainder 46
2 104 ÷ 46 = 2 remainder 12
3 46 ÷ 12 = 3 remainder 10
4 12 ÷ 10 = 1 remainder 2
5 10 ÷ 2 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
169 and 941
132 and 1611
135 and 1455
150 and 862
178 and 1331

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