Greatest Common Divisor (GCD) of 107 and 160
The greatest common divisor (GCD) of 107 and 160 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 107 and 160?
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 | 107 ÷ 160 = 0 remainder 107 |
| 2 | 160 ÷ 107 = 1 remainder 53 |
| 3 | 107 ÷ 53 = 2 remainder 1 |
| 4 | 53 ÷ 1 = 53 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 187 and 109 | 1 |
| 176 and 178 | 2 |
| 103 and 19 | 1 |
| 122 and 74 | 2 |
| 131 and 179 | 1 |