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Greatest Common Divisor (GCD) of 16 and 91

The greatest common divisor (GCD) of 16 and 91 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 16 and 91?

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 16 ÷ 91 = 0 remainder 16
2 91 ÷ 16 = 5 remainder 11
3 16 ÷ 11 = 1 remainder 5
4 11 ÷ 5 = 2 remainder 1
5 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
146 and 1842
122 and 1082
126 and 1851
23 and 791
179 and 1281

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