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Greatest Common Divisor (GCD) of 63 and 61

The greatest common divisor (GCD) of 63 and 61 is 1.

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 61?

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 ÷ 61 = 1 remainder 2
2 61 ÷ 2 = 30 remainder 1
3 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
113 and 751
176 and 176176
96 and 651
157 and 1211
177 and 1893

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