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Greatest Common Divisor (GCD) of 130 and 63

The greatest common divisor (GCD) of 130 and 63 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 130 and 63?

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
1 130 ÷ 63 = 2 remainder 4
2 63 ÷ 4 = 15 remainder 3
3 4 ÷ 3 = 1 remainder 1
4 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
94 and 1391
199 and 171
143 and 961
45 and 171
22 and 462

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