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Greatest Common Divisor (GCD) of 152 and 111

The greatest common divisor (GCD) of 152 and 111 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 111?

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 ÷ 111 = 1 remainder 41
2 111 ÷ 41 = 2 remainder 29
3 41 ÷ 29 = 1 remainder 12
4 29 ÷ 12 = 2 remainder 5
5 12 ÷ 5 = 2 remainder 2
6 5 ÷ 2 = 2 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
165 and 531
183 and 1563
176 and 364
14 and 502
24 and 753

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