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Greatest Common Divisor (GCD) of 63 and 96

The greatest common divisor (GCD) of 63 and 96 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 63 and 96?

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 63 ÷ 96 = 0 remainder 63
2 96 ÷ 63 = 1 remainder 33
3 63 ÷ 33 = 1 remainder 30
4 33 ÷ 30 = 1 remainder 3
5 30 ÷ 3 = 10 remainder 0

Examples of GCD Calculations

NumbersGCD
123 and 603
121 and 501
122 and 742
83 and 321
24 and 611

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