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Greatest Common Divisor (GCD) of 110 and 35

The greatest common divisor (GCD) of 110 and 35 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 35?

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 ÷ 35 = 3 remainder 5
2 35 ÷ 5 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
176 and 1291
62 and 1362
70 and 14070
30 and 19515
56 and 1791

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