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Greatest Common Divisor (GCD) of 161 and 44

The greatest common divisor (GCD) of 161 and 44 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 161 and 44?

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
1 161 ÷ 44 = 3 remainder 29
2 44 ÷ 29 = 1 remainder 15
3 29 ÷ 15 = 1 remainder 14
4 15 ÷ 14 = 1 remainder 1
5 14 ÷ 1 = 14 remainder 0

Examples of GCD Calculations

NumbersGCD
15 and 1173
184 and 1771
36 and 1818
194 and 622
127 and 351

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