Greatest Common Divisor (GCD) of 113 and 161
The greatest common divisor (GCD) of 113 and 161 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 113 and 161?
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 | 113 ÷ 161 = 0 remainder 113 |
| 2 | 161 ÷ 113 = 1 remainder 48 |
| 3 | 113 ÷ 48 = 2 remainder 17 |
| 4 | 48 ÷ 17 = 2 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 161 and 34 | 1 |
| 31 and 89 | 1 |
| 161 and 123 | 1 |
| 136 and 180 | 4 |
| 189 and 92 | 1 |