Greatest Common Divisor (GCD) of 110 and 139
The greatest common divisor (GCD) of 110 and 139 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 110 and 139?
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 | 110 ÷ 139 = 0 remainder 110 |
| 2 | 139 ÷ 110 = 1 remainder 29 |
| 3 | 110 ÷ 29 = 3 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 108 and 200 | 4 |
| 168 and 88 | 8 |
| 182 and 169 | 13 |
| 168 and 121 | 1 |
| 83 and 189 | 1 |