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Greatest Common Divisor (GCD) of 137 and 148

The greatest common divisor (GCD) of 137 and 148 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 137 and 148?

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
1 137 ÷ 148 = 0 remainder 137
2 148 ÷ 137 = 1 remainder 11
3 137 ÷ 11 = 12 remainder 5
4 11 ÷ 5 = 2 remainder 1
5 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
69 and 813
121 and 1931
29 and 951
74 and 1282
124 and 1604

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