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Greatest Common Divisor (GCD) of 88 and 56

The greatest common divisor (GCD) of 88 and 56 is 8.

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 88 and 56?

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 88 ÷ 56 = 1 remainder 32
2 56 ÷ 32 = 1 remainder 24
3 32 ÷ 24 = 1 remainder 8
4 24 ÷ 8 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
45 and 1481
175 and 1911
184 and 1191
63 and 1359
113 and 431

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