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Greatest Common Divisor (GCD) of 144 and 29

The greatest common divisor (GCD) of 144 and 29 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 144 and 29?

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
1 144 ÷ 29 = 4 remainder 28
2 29 ÷ 28 = 1 remainder 1
3 28 ÷ 1 = 28 remainder 0

Examples of GCD Calculations

NumbersGCD
145 and 231
129 and 531
35 and 761
136 and 1711
159 and 1173

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