Greatest Common Divisor (GCD) of 87 and 116
The greatest common divisor (GCD) of 87 and 116 is 29.
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 116?
We use the Euclidean algorithm, which involves the following steps:
- Divide the larger number by the smaller number.
- Replace the larger number with the smaller number and the smaller number with the remainder from the division.
- Repeat this process until the remainder is zero.
- The non-zero remainder just before zero is the GCD.
Step-by-Step Euclidean Algorithm
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 116 = 0 remainder 87 |
| 2 | 116 ÷ 87 = 1 remainder 29 |
| 3 | 87 ÷ 29 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 111 and 30 | 3 |
| 124 and 105 | 1 |
| 163 and 109 | 1 |
| 76 and 89 | 1 |
| 34 and 157 | 1 |