Greatest Common Divisor (GCD) of 68 and 187
The greatest common divisor (GCD) of 68 and 187 is 17.
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 68 and 187?
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 | 68 ÷ 187 = 0 remainder 68 |
| 2 | 187 ÷ 68 = 2 remainder 51 |
| 3 | 68 ÷ 51 = 1 remainder 17 |
| 4 | 51 ÷ 17 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 135 and 87 | 3 |
| 113 and 109 | 1 |
| 64 and 164 | 4 |
| 139 and 93 | 1 |
| 151 and 181 | 1 |