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Greatest Common Divisor (GCD) of 154 and 141

The greatest common divisor (GCD) of 154 and 141 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 154 and 141?

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
1 154 ÷ 141 = 1 remainder 13
2 141 ÷ 13 = 10 remainder 11
3 13 ÷ 11 = 1 remainder 2
4 11 ÷ 2 = 5 remainder 1
5 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
77 and 1811
95 and 1231
165 and 611
140 and 1197
114 and 1462

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