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Greatest Common Divisor (GCD) of 146 and 125

The greatest common divisor (GCD) of 146 and 125 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 146 and 125?

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
1 146 ÷ 125 = 1 remainder 21
2 125 ÷ 21 = 5 remainder 20
3 21 ÷ 20 = 1 remainder 1
4 20 ÷ 1 = 20 remainder 0

Examples of GCD Calculations

NumbersGCD
63 and 221
22 and 1842
45 and 7515
29 and 1491
69 and 1331

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