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Greatest Common Divisor (GCD) of 33 and 15

The greatest common divisor (GCD) of 33 and 15 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 33 and 15?

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 33 ÷ 15 = 2 remainder 3
2 15 ÷ 3 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
69 and 1773
54 and 12618
143 and 171
122 and 1482
78 and 1062

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