Greatest Common Divisor (GCD) of 140 and 102
The greatest common divisor (GCD) of 140 and 102 is 2.
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 140 and 102?
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 | 140 ÷ 102 = 1 remainder 38 |
| 2 | 102 ÷ 38 = 2 remainder 26 |
| 3 | 38 ÷ 26 = 1 remainder 12 |
| 4 | 26 ÷ 12 = 2 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 37 and 47 | 1 |
| 131 and 50 | 1 |
| 10 and 13 | 1 |
| 135 and 95 | 5 |
| 154 and 117 | 1 |