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Greatest Common Divisor (GCD) of 144 and 49

The greatest common divisor (GCD) of 144 and 49 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 49?

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 ÷ 49 = 2 remainder 46
2 49 ÷ 46 = 1 remainder 3
3 46 ÷ 3 = 15 remainder 1
4 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
55 and 191
132 and 262
31 and 6231
74 and 1451
145 and 1971

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