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Greatest Common Divisor (GCD) of 157 and 156

The greatest common divisor (GCD) of 157 and 156 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 157 and 156?

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
1 157 ÷ 156 = 1 remainder 1
2 156 ÷ 1 = 156 remainder 0

Examples of GCD Calculations

NumbersGCD
121 and 1041
161 and 1781
102 and 813
134 and 951
149 and 1841

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