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Greatest Common Divisor (GCD) of 187 and 48

The greatest common divisor (GCD) of 187 and 48 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 187 and 48?

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
1 187 ÷ 48 = 3 remainder 43
2 48 ÷ 43 = 1 remainder 5
3 43 ÷ 5 = 8 remainder 3
4 5 ÷ 3 = 1 remainder 2
5 3 ÷ 2 = 1 remainder 1
6 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
162 and 10854
93 and 1361
167 and 891
67 and 791
15 and 441

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