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Greatest Common Divisor (GCD) of 87 and 100

The greatest common divisor (GCD) of 87 and 100 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 87 and 100?

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 87 ÷ 100 = 0 remainder 87
2 100 ÷ 87 = 1 remainder 13
3 87 ÷ 13 = 6 remainder 9
4 13 ÷ 9 = 1 remainder 4
5 9 ÷ 4 = 2 remainder 1
6 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
128 and 751
67 and 1011
108 and 1413
190 and 1322
92 and 1724

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