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Greatest Common Divisor (GCD) of 29 and 100

The greatest common divisor (GCD) of 29 and 100 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 29 and 100?

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 29 ÷ 100 = 0 remainder 29
2 100 ÷ 29 = 3 remainder 13
3 29 ÷ 13 = 2 remainder 3
4 13 ÷ 3 = 4 remainder 1
5 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
178 and 1711
128 and 1164
179 and 1141
99 and 981
39 and 981

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