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Greatest Common Divisor (GCD) of 145 and 65

The greatest common divisor (GCD) of 145 and 65 is 5.

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 145 and 65?

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
1 145 ÷ 65 = 2 remainder 15
2 65 ÷ 15 = 4 remainder 5
3 15 ÷ 5 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
38 and 1942
119 and 691
102 and 573
49 and 1511
191 and 751

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