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Greatest Common Divisor (GCD) of 152 and 115

The greatest common divisor (GCD) of 152 and 115 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 152 and 115?

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
1 152 ÷ 115 = 1 remainder 37
2 115 ÷ 37 = 3 remainder 4
3 37 ÷ 4 = 9 remainder 1
4 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
18 and 1293
181 and 1331
18 and 1746
105 and 1197
146 and 1551

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