Greatest Common Divisor (GCD) of 187 and 113
The greatest common divisor (GCD) of 187 and 113 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 187 and 113?
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 | 187 ÷ 113 = 1 remainder 74 |
| 2 | 113 ÷ 74 = 1 remainder 39 |
| 3 | 74 ÷ 39 = 1 remainder 35 |
| 4 | 39 ÷ 35 = 1 remainder 4 |
| 5 | 35 ÷ 4 = 8 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 70 and 175 | 35 |
| 176 and 98 | 2 |
| 198 and 11 | 11 |
| 114 and 118 | 2 |
| 110 and 42 | 2 |