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Greatest Common Divisor (GCD) of 91 and 151

The greatest common divisor (GCD) of 91 and 151 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 91 and 151?

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 91 ÷ 151 = 0 remainder 91
2 151 ÷ 91 = 1 remainder 60
3 91 ÷ 60 = 1 remainder 31
4 60 ÷ 31 = 1 remainder 29
5 31 ÷ 29 = 1 remainder 2
6 29 ÷ 2 = 14 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
158 and 702
165 and 921
157 and 1031
41 and 941
146 and 1411

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