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Greatest Common Divisor (GCD) of 63 and 178

The greatest common divisor (GCD) of 63 and 178 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 178?

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 ÷ 178 = 0 remainder 63
2 178 ÷ 63 = 2 remainder 52
3 63 ÷ 52 = 1 remainder 11
4 52 ÷ 11 = 4 remainder 8
5 11 ÷ 8 = 1 remainder 3
6 8 ÷ 3 = 2 remainder 2
7 3 ÷ 2 = 1 remainder 1
8 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
138 and 1626
32 and 924
116 and 244
81 and 1811
137 and 1221

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