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Greatest Common Divisor (GCD) of 110 and 65

The greatest common divisor (GCD) of 110 and 65 is 5.

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 110 and 65?

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
1 110 ÷ 65 = 1 remainder 45
2 65 ÷ 45 = 1 remainder 20
3 45 ÷ 20 = 2 remainder 5
4 20 ÷ 5 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
160 and 782
88 and 1631
26 and 502
39 and 14313
40 and 488

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